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According to the Russian consulate in Hong Kong:
APEC Business Travel Card (ABTC) holders with “RUS” inscribed on the back enjoy a visa-free entry into Russia for official or business visits. While passing Russian border control ABTC holders need to present their valid national passport and the valid ABTC.
Total period of stay in the Russian Federation can be no more than 90 days during any period of 180 days.
Note: cardholders travelling to Russia for other purposes need to make a respective Russian visa.
The underlying law (Executive Order #777) likewise fails to mention any documents besides a passport and a valid APEC card.
So as long as you're traveling for business you're not obligated to carry any other papers. How you prove that you're actually a businessman if challenged by the border guards is up to you - I assume informal proof such as a printed email or a local contact's business card should be sufficient.