It's not really a 'game' in the sense of there being points to be scored or winners and losers at the end, more it's the social conventions that make the workplace pleasant (according to what the majority/ conventions define as pleasant, which can vary from what you individually prefer).
It's things like taking an interest in your co-workers lives, their spouses and children, what they watch on TV, where they are going on holiday (but not too much interest as that would also be weird), and sharing similar information about yourself - essentially forming a social relationship/ bond with people that if you weren't colleagues you would not have any kind of relationship with. Workplace gossip is an interesting one - you may really not care about the spat Tim and John had over the photocopier or that Tina resents Rachel's promotion (if these things don't affect you in any way) but it is part of the convention (or game if you will) to pay at least lip service to this being interesting and significant news - if you are too open about your disdain for such things it will definitely be interpreted (probably correctly) as disdain for your colleagues or thinking that you are better than them - it's just not the done thing.
It's sort of like grooming or other bonding behaviours animals do - it may not be strictly necessary for survival but it creates social bonds. Most people (not all) value those bonds and find people who voluntarily place themselves outside the group norm in that way somehow odd or suspicious or think they're looking down on them.
Not saying that to 'play the game' means you suddenly have to be Queen Bee of the workplace, spending every moment and chatting and gossiping and so on, and you definitely don't have to be bitchy (speaking as a socially awkward person putting on a fake act in that way is just as bad if not worse than being your unvarnished 'real self'). But it's good to show a token interest, inconsequential small talk is great, as is asking questions - the latter I find particularly good in case of gossip, as like you i really don't like to participate in anything hurtful, so if someone comes in going 'OMG did you hear about how Ann embarrassed herself' I'll say things like 'what happened', 'is she OK', things like that, rather than refusing to participate in the conversation at all, but I won't join in merely slagging Ann off - if the conversation goes that way I'll either change the subject or if need be invent a reason I need to leave the conversation entirely.