Games that have batteries on them usually use rechargable batteries, often nicads, usually 3.6v, and usually somewhere around 150 milli-amp hours. A A cordless phone battery is usually 3.6v, nicad, and about 3000 milli-amp hours. Which means it's basically the same thing, just in a higher capacity. So it charges in exactly the same way the original battery did, with no modifications.
I personally did this to a couple of games, but later switched to a diode with a lithium coin cell, because the remoted battery was a pain for getting the boards out. That's just a matter of preference, though - different folks like different things.