The V2 electronics can be used in the 4 line character screen (it's done like that for the UMO+)
The game won't work there. Because it requires the UM2 display (full graphical)
The 1.5.7 electronics has a heated bed connection, however, you should not use it. The power supply connector and traces where not properly designed and cannot handle the amount of power needed for a heated bed.
I would not recommend the 1.5.7 electronics for any new build. The V2 simply saves you a lot of trouble.
Connecting a themistor to the V2 electronics is a bit more work. As the default temperature measure circuit is build for PT100. But there are analog pins available on the board that you can use for everything you want.
There is ALWAYS room for a game :-)
(It's hidden in the code, does not use any extra ram, and only like 2k of flash, which there is more then enough of in the UM2)