Can a Russian citizen enter Gibraltar with an EU residence permit?

No, just as a Schengen resident permit does not exempt someone from the UK Standard Visitor visa requirement, the Gibraltar Immigration, Asylum And Refugee Act, 1962-12 forsee's no exception - despite the fact that certain holders (presently: nationals of Morocco, the People’s Republic of China, Mongolia, India or Russia) of a valid multiple entry Schengen Visas are exempt.

Only non-EEA national family members, that otherwise requires a visa, are exempt from a Gibraltar Visitor Visa.

Immigration, Asylum And Refugee Act, 1962-12

• Commencement date: 2016-10-06 (latest version as of 2020-10-26)

Application: EEA Nationals and their family members
3.
The provisions of sections 6, 7(2), 12(1), 14(1) and (2), 15 to 38, 52, 53 and 64 shall not apply to any person to whom, for the time being, sections 55A to 55X apply.
...
Entry into and exit from Gibraltar.
11.
No person who seeks to enter or exit Gibraltar overland shall enter or exit other than–

(a) through the pedestrian or vehicular gates at the frontier, or
(b) through the commercial gates at the frontier at a time when it is open for authorized commercial traffic under the supervision and control of an immigration officer.

11A.
(1) The Government may direct the Principal Immigration Officer to waive the carrying out in circumstances described in such directions of any controls, powers or functions required or permitted under this Act on any persons or category of persons who enter or leave Gibraltar or who are in transit by land, sea or air through the airport to any other country specified in such direction.
(2) A direction under sub-section (1) may include a waiver of the requirement to be in possession of a valid entry permit under section 12(1) and upon the issue of any such direction, the provisions of section 12(1) shall not apply to any person to whom the direction relates to the extent that it requires such person to be in possession of a valid entry permit.
(3) Any direction issued under sub-section (1) may be revoked or modified by the Government at any time and from time to time and may impose restrictions on the period that such persons or categories of person may remain in Gibraltar.
(3A)
Any direction under subsection (1) which relates to a category of persons described by virtue of their being nationals of particular countries who hold valid multiple entry Schengen Visas shall be published in the Gazette.
(3B)
Any direction under subsection (1) to which subsection (3A) applies shall−
(a) include a waiver under subsection (2) of the requirement to be in possession of a valid entry permit under section 12(1);
(b) confirm that a waiver issued under subsection (2) does not entitle the holder to seek employment in Gibraltar or entitle him to have access to publicly funded benefits in Gibraltar;
(c) specify a period that such a person is authorised to remain in Gibraltar which shall not exceed−

(i) 21 days; or
(ii) where the multiple entry Schengen Visa is due to expire before 21 days from the entry of the person into Gibraltar, the remainder of the period of validity of such multiple entry Schengen Visa less 7 days.

...
EEA Rights – Entry and Residence.
Right of Entry to Gibraltar.
55J.
(1) An EEA national shall be allowed to enter Gibraltar if he produces on arrival a valid passport or identity card issued by an EEA state.
(2) A non-EEA national shall be allowed to enter Gibraltar if he is the family member of an EEA national, a family member who has retained the right of residence or a person with a permanent right of residence under section 55N if he produces on arrival–

(a) a valid passport; and
(b) an EEA family permit, a residence card or a permanent residence card.

(3) An entry or exit stamp shall not be placed in the passport of a person allowed to enter Gibraltar under this section if-

(a) he is an EEA national; or
(b) he is a non-EEA national who produces a residence card or permanent residence card.

...
Entitlement to reside in Gibraltar for three months
55L.
(1) The following persons are entitled to reside in Gibraltar for a period not exceeding three months from the date of entry into Gibraltar–

(a) an EEA national who holds a valid passport or identity card issued by an EEA state;
(b) a non-EEA national who-

• (i) is a family member of an EEA national residing in Gibraltar under paragraph (a); and
• (ii) holds a valid passport.

Note:
A Schengen visa is a short stay visa allowing its holder to circulate in the Schengen area, based on Article 2(5) (Type A) and Article 2(2) (Type C) of the Schengen Border Code.

A national long-stay visa (Type D, ANNEX VII (7 type of visa) of the Schengen Border Code) is not a Schengen Visa, but a National Visa.

Sources:

• Immigration, Asylum And Refugee Act, 1962-12 [2016-10-06]
  • Visas and Immigration
    • 2020-10-26: This site is currently being revised
  • Gibraltar Borders & Coast Guard Agency - Visa & Entry

Today: A German residence permit will not be enough to enter Gibraltar for a Russian citizen. In normal circumstances, a visa is needed to access Gibraltar unless the Russian citizen holds a EU family permit.

Covid-19 situation. Due to Covid situation in Spain only EU citizens or holders of EU Family permit can access Gibraltar via the Spanish border. Citizens that hold a EU family permit can also access it. https://makespain.com/gibraltar-city-guide/

Due to COVID-19 no access was possible through Spain till July unless the person accessing Gibraltar held a working permission (a working contract) in Gibraltar. Due to the evolution of the Covid-measures in all regions in Spain, this restriction could be back in place. Please note this does not depend on Gibraltar authorities only.

Brexit also adds complexity. It is not clear if Gibraltar will be part of Schengen after Brexit. Gibraltar has requested this. This could imply a different reality to a Russian citizen with working permission in Germany but it is so far unclear https://www.etiasvisa.com/etias-news/etias-gibraltar

I've contacted the Borders & Coastguard Agency of Gibraltar with exactly the case described above and have received the following answer:

We do not accept residency cards issued outside of the United Kingdom unless they have been issued on the basis that the holder is a family member of an EU National. For us to accept the residency card it would need to state clearly that the holder is a family member.

If the card has not been issued on this basis and you are a family member of an EU National and reside in an EU State together then we would accept an original marriage certificate, if the certificate is not in the English language then a copy must also be provided of a translation authorised by a notary.

If none of the above apply to you or visitor and you are in fact a visa requiring national for Gibraltar then we would accept a UK Multiple entry 6 month Visitor visa or alternatively a UK Gibraltar Overseas territory visa.

From this answer, it seems that while most countries do consider an EU residence permit equivalent to a Schengen visa (if it was issued in a Schengen country), this does not apply to Gibraltar, even if the holder of the EU residence permit is a national of Russia, China, Morocco, Mongolia or India. That means a separate UK or Gibraltar visa is required.

(This of course creates the curious circumstance that a Russian national living in a Schengen country can invite and sponsor another Russian to get a Schengen visitor visa (which allows them to enter Gibraltar), but cannot enter it themselves.)