Would an American who lives in Japan be allowed into the Schengen Zone for non-essential travel?

TL;DR: you would probably not be allowed in for Germany, but worth trying to confirm with German authorities. Below is for Germany but you can check other EU countries the same way.

reopen.europa.eu info for Germany:

As a third-country national coming from outside the EU and Norway,
Switzerland, Iceland and Liechtenstein, may I enter this country
without exceptional restrictions?

YES, WITH LIMITATION. Travellers from
Australia, Georgia, Canada, Montenegro, New Zealand, Thailand, Tunisia
and Uruguay will be able to enter without restrictions from 2 July.
That will also apply to Japan, South Korea and China — but only if
those countries also allow people from Germany to enter. For the
determination of the entry possibility, the previous location of the
travelers is decisive, not their nationality. Regardless of the entry
options in Germany, a quarantine obligation based on the Infection
Protection Act applies in all federal states for incoming and
returning travelers from the risk areas specified by the RKI. With the
exception of passengers in transit traffic, this also applies in
principle to travelers with an important travel reason. An exception
to the quarantine applies to the current negative test. The most
important goal of all considerations remains to secure the further
containment of the pandemic.

Last update: 01-07-2020

See https://www.iatatravelcentre.com/international-travel-document-news/1580226297.htm whether Japan refuse travelers from Germany (depends to whom you’re married to, e.g. looks like Japan accepts travelers from Germany if spouse of nationals of Japan, but since Japan doesn’t accept most/all travelers from Japan, German maturely reciprocate by also not allowing travelers from Japan).

https://www.iatatravelcentre.com/international-travel-document-news/1580226297.htm for Japan:

Published 01.07.2020

1. Passengers who have transited through or have been in Afghanistan, Albania, Algeria, Andorra, Antigua and Barbuda, Argentina, Armenia, Australia, Austria, Azerbaijan, Bahamas, Bahrain, Bangladesh, Barbados, Belarus, Belgium, Bolivia, Bosnia and Herzegovina, Brazil, Brunei Darussalam, Bulgaria, Cameroon, Canada, Cape Verde, Central African Rep., Chile, China (People’s Rep.), Chinese Taipei, Congo (Dem. Rep.), Colombia, Costa Rica, Cote d’Ivoire, Croatia, Cuba, Cyprus, Czechia, Denmark, Djibouti, Dominica, Dominican Rep., Ecuador, Egypt, El Salvador, Equatorial Guinea, Estonia, Eswatini, Finland, France, Gabon, Georgia, Germany, Ghana, Greece, Grenada, Guatemala, Guinea, Guinea-Bissau, Guyana, Haiti, Honduras, Hong Kong (SAR China), Hungary, Iceland, India, Indonesia, Iran, Iraq, Ireland (Rep.), Israel, Italy, Jamaica, Kazakhstan, Korea (Rep.), Kosovo (Rep.), Kuwait, Kyrgyzstan, Latvia, Lebanon, Liechtenstein, Lithuania, Luxembourg, Macao (SAR China), Malaysia, Maldives, Malta, Mauritania, Mauritius, Mexico, Moldova (Rep.), Monaco, Montenegro, Morocco, Netherlands, New Zealand, Nicaragua, North Macedonia (Rep.), Norway, Oman, Pakistan, Panama, Peru, Philippines, Poland, Portugal, Qatar, Romania, Russian Fed., San Marino, Sao Tome and Principe, Saudi Arabia, Senegal, Serbia, Singapore, Slovakia, Slovenia, South Africa, Spain, St. Kitts and Nevis, St. Vincent and the Grenadines, Sweden, Switzerland, Tajikistan, Thailand, Turkey, Uruguay, USA, Ukraine, United Arab Emirates, United Kingdom, Vatican City (Holy See) or Viet Nam in the past 14 days are not allowed to enter until 31 July 2020.
   • This does not apply to nationals of Japan.
   • This does not apply to spouses or children of nationals of Japan if they can prove it.
   • This does not apply to residents of Japan with “Permanent Resident", "Spouse or Child of Japanese National", "Spouse or Child of Permanent Resident" or "Long Term Resident", who have departed Japan with Re-entry Permission by 2 April 2020.
   • This does not apply to residents of Japan with “Permanent Resident", "Spouse or Child of Japanese National", "Spouse or Child of Permanent Resident" or "Long Term Resident", who have departed Japan with Re-entry Permission between 3 April and 28 April 2020 and have only been in Afghanistan, Antigua and Barbuda, Argentina, Azerbaijan, Bahamas, Bangladesh, Barbados, Belarus, Cape Verde, Colombia, Djibouti, Dominican Rep., El Salvador, Equatorial Guinea, Gabon, Ghana, Guinea, Guinea Bissau, Honduras, India, Kazakhstan, Kuwait, Kyrgyzstan, Mexico, Maldives, Oman, Pakistan, Peru, Qatar, Russian Fed., Sao Tome and Principe, Saudi Arabia, South Africa, St. Kitts and Nevis, Tajikistan, United Arab Emirates, Ukraine or Uruguay.
   • This does not apply to residents of Japan with “Permanent Resident", "Spouse or Child of Japanese National", "Spouse or Child of Permanent Resident" or "Long Term Resident", who have departed Japan with Re-entry Permission between 29 April and 15 May 2020 and have only been in Afghanistan, Argentina, Azerbaijan, Bahamas, Bangladesh, Cape Verde, Colombia, El Salvador, Equatorial Guinea, Gabon, Ghana, Guinea, Guinea Bissau, Honduras, India, Kazakhstan, Kyrgyzstan, Mexico, Maldives, Pakistan, South Africa, Sao Tome and Principe, Tajikistan or Uruguay.
   • This does not apply to residents of Japan with “Permanent Resident", "Spouse or Child of Japanese National", "Spouse or Child of Permanent Resident" or "Long Term Resident", who have departed Japan with Re-entry Permission between 16 May and 26 May 2020 and have only been in Afghanistan, Argentina, Bangladesh, El Salvador, Ghana, Guinea, India, Kyrgyzstan, Pakistan, South Africa or Tajikistan.
   • This does not apply to residents of Japan with “Permanent Resident", "Spouse or Child of Japanese National", "Spouse or Child of Permanent Resident" or "Long Term Resident", who have departed Japan with Re-entry Permission between 27 May and 30 June 2020 and have only been in Algeria, Cameroon, Central African Rep., Costa Rica, Cuba, Eswatini, Georgia, Grenada, Guatemala, Guyana, Haiti, Iraq, Jamaica, Lebanon, Mauritania, Nicaragua, Senegal or St. Vincent and the Grenadines.
   • This does not apply to passengers with a Special Permanent Residence Permit. However, they must have a Re-entry Permit from a regional immigration officer.
   • This does not apply to US military personnel.
2. A completed "Quarantine Questionnaire" must be presented upon arrival.
3. Passengers and airline crew are subject to medical screening.
4. Visa exemption for passengers with passengers with a British passport, Hong Kong (SAR China) passport, Macao (SAR China) passport is suspended.
5. Visa exemption for nationals of Andorra, Argentina, Austria, Bahamas, Barbados, Belgium, Brunei Darussalam, Bulgaria, Costa Rica, Croatia, Czechia, Cyprus, Denmark, Dominican Rep., El Salvador, Estonia, Finland, France, Germany, Greece, Guatemala, Honduras, Hungary, Iceland, Indonesia, Iran, Ireland (Rep.), Israel, Italy, Korea (Rep.), Latvia, Lesotho, Liechtenstein, Lithuania, Luxembourg, Malaysia, Malta, Mexico, Monaco, Netherlands, Norway, Peru, Poland, Portugal, Romania, San Marino, Singapore, Slovakia, Slovenia, Spain, Suriname, Sweden, Switzerland, Thailand, Tunisia, United Arab Emirates, Uruguay and Vatican City (Holy See) is suspended.
6. Visa exemption for nationals of Azerbaijan, Bangladesh, Cambodia, Colombia, Georgia, India, Kazakhstan, Lao People’s Dem. Rep., Mongolia, Myanmar, Nauru, Oman, Pakistan, Palau, Papua New Guinea, Paraguay, Qatar, Samoa, Solomon Isl., Turkmenistan, Ukraine, Uzbekistan and Viet Nam with a diplomatic, official or service passport is suspended.
7. Visa exemption granted to passengers with an APEC Business Travel Card issued by Brunei Darussalam, China (People’s Rep.), Hong Kong (SAR China), Indonesia, Korea (Rep.), Malaysia, Mexico, Papua New Guinea, Peru, Philippines, Russian Fed., Singapore, Thailand or Viet Nam, is suspended.
8. Nationals of China (People’s Rep.) with a passport issued in Hubei Province or Zhejiang Province (China People’s Rep.) are not allowed to enter Japan.
   • This does not apply when passengers can prove that they have not been in Hubei Province and Zhejiang Province the last 14 days.
9. Passengers who were in the cruise ship ‘Westerdam’ are not allowed to enter Japan.
   • This does not apply to nationals of Japan.
10. Visas issued on or before 8 March 2020 by the Embassies, Consulates-General and Consulate of Japan in China (People’s Rep.), Hong Kong (SAR China), Korea (Rep.) or Macao (SAR China) are invalidated.
11. Visas issued on or before 20 March 2020 by the Embassies, Consulates-General and Consulate of Japan in Andorra, Austria, Belgium, Bulgaria, Croatia, Czechia, Cyprus, Denmark, Egypt, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Iran, Ireland (Rep.), Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Monaco, Netherlands, Norway, Poland, Portugal, Romania, San Marino, Slovakia, Slovenia, Spain, Sweden, Switzerland, United Kingdom or Vatican City (Holy See) are invalidated.
12. Visas issued on or before 27 March 2020 by the Embassies, Consulates-General and Consulate of Japan in Bahrain, Brunei Darussalam, Congo (Dem. Rep.), Indonesia, Israel, Malaysia, Philippines, Qatar, Singapore, Thailand or Viet Nam are invalidated.
13. Visas issued on or before 2 April 2020 by the Embassies, Consulates-General and Consulate of Japan in Afghanistan, Algeria, Angola, Antigua and Barbuda, Argentina, Azerbaijan, Bahamas, Bangladesh, Barbados, Belarus, Belize, Benin, Bhutan, Botswana, Burkina Faso, Burundi, Cambodia, Cameroon, Cape Verde, Central African Rep., Chad, Colombia, Comoros, Congo, Cook Isl., Costa Rica, Cuba, Djibouti, Dominican Rep., El Salvador, Equatorial Guinea, Eritrea, Eswatini (Swaziland), Ethiopia, Fiji, Gabon, Gambia, Georgia, Ghana, Grenada, Guatemala, Guinea, Guinea-Bissau, Guyana, Haiti, Honduras, India, Iraq, Jamaica, Jordan, Kazakhstan, Kenya, Kiribati, Kyrgyzstan, Kuwait, Lao People’s Dem. Rep., Lebanon, Lesotho, Liberia, Libya, Madagascar, Malawi, Maldives, Mali, Marshall Isl., Mauritania, Mexico, Micronesia (Federated States), Mongolia, Mozambique, Myanmar, Namibia, Nauru, Nepal, Nicaragua, Niger, Nigeria, Niue, Oman, Pakistan, Palau, Palestinian Territory, Papua New Guinea, Paraguay, Peru, Russian Fed., Rwanda, Samoa, Sao Tome and Principe, Saudi Arabia, Senegal, Seychelles , Sierra Leone, Solomon Isl., Somalia, South Africa, South Sudan, Sri Lanka, St. Kitts and Nevis, St. Lucia, St. Vincent and Grenadines, Sudan, Suriname, Syria, Tajikistan, Tanzania, Timor-Leste, Togo, Tonga, Trinidad and Tobago, Tunisia, Turkmenistan, Tuvalu, Uganda, Ukraine, United Arab Emirates, Uruguay, Uzbekistan, Vanuatu, Venezuela, Yemen, Zambia or Zimbabwe are invalidated.
14. Passengers transiting through Tokyo (NRT) must transit on the same calendar day.