Preventive blocking the game with the firewall is always a good idea.
But checking if the game ... that's another story. There is no generic and simple solution. Also, there is a cost: security vs usability. My method:
I use a firewall in interactive mode. This means every time a new program tries to connect to a site, the firewall put an info window in foreground and I decide what to do: allow, forbid, make a permanent rule etc. This is a very annoying solution for most of people, especially for normal users, but works for me (yeah, I'm paranoid, but am I paranoid enough?
).
And speaking about games:
Majority of Unity games use Unity analytics. These means the game sends data silently, in background, for analytic purposes. Few developers advertise this.