You are correct.
One can solder in a temporary "helper battery" (or 3V power supply) to the same traces but in a different spot, to keep the SRAM alive while the real battery is replaced.
Some later games (GBA-era) use Flash memory and the battery is just for the clock.
I went to school in the '90s. My friend and I thought the Game Boy game Final Fantasy Legend II was funny in the way that you fought against terrorists, dinosaurs, ghosts, robots, and germs, using magic and medieval-fantasy-trope weapons alongside muskets, SMGs, chainsaws, and even nukes! (Game devs and translators had to get creative with only seven letters and an item type symbol for the item names, to fit in the tiny amount of memory available.)
Our drawings inspired by this were often battle scenes with the likes of Hussein, Hitler, and Mussolini being shot, impaled, nuked, and/or decapitated by chainsaw. We must have drawn a thousand guns.
We turned out OK.
Final Fantasy Legend spoiler alert
Years later, I played through Final Fantasy Legend 1 and discovered that even the final boss can fall to the Chainsaw (a weapon with a low chance of instant kill). The battle log says "Creator went to pieces!"
Killed God with a chainsaw.