Yep, it is a BR battery. Not sure about the position of the tabs, but as far as I know, CR and BR are both fine, they are just designed for slightly different kinds of circuits. Either should work in this case. A CR battery's voltage drops uniformly over time whereas BR maintains a pretty steady voltage over its life, but then drops suddenly at the end of its life. Check out the very bottom of this page: http://www.swcomputingservices.com/batteryorder.html.
I used the BR2032 from digikey and my games seem to be working fine so far.