After the discovery of the monolith / obelisk and the fact that Jupiter and Saturn will soon be in alignment, it occurred to me that the marker "shall we play a nice game of chess" could also be referencing the movie "2010: The Year We Make Contact", it's the sequel to "Odyssey 2001".
In the move "War Games" the computer asks "Shall we play a game? … Wouldn't you prefer a good game of chess?" (roughly 40 mins into the movie), in 2010 Hal-9000 asks Dr. Floyd "Would you like to play a game of chess?" (roughly 1:21:00 into the movie).
It is interesting, since in a way 2010 is about a potential nuclear stand-off between Russia and the US and backchannels to cooperate and ultimately save the ship and deliver a message of peace to mankind.