I'm not sure what "game" means in the following context.
Search engine optimization(SEO) is an endless battle between Google, which wants to have the highest quality results for its users and advertisers, and SEO experts who try to game the algorithms. ...
But in the end, SEO is more about making good stuff that people actually want to look at than gaming Google's algorithms.
It means, roughly, "to take advantage of" the system. To treat the situation as a "game" and to try to win.
People want their websites to show up first when someone does a Google search. Google tries to write algorithms to show the most useful or popular sites. People try to analyze the algorithms and figure out what coding magic to use to make Google's algorithms display their pages in the search results.