This set looks to be the same meter, currently $20 in my area. Good luck!

Interesting question.

I don't have an answer to what extent different games affect current draw, but I do have some general thoughts:

The draw will likely vary to some extent based on the particular chips used by a specific game. Extra components like rumble, photo sensors, tilt sensors, etc, will increase draw, and flash carts will draw more power than a rom cart.

The RTC battery shouldn't be supplying any voltage to the Gameboy, or vise versa, so whether a game uses a RTC shouldn't have any impact on battery life by itself.

The best way to find out is to test it yourself. If you're interested in any sort of electrical projects (like console modding) a multimeter (like this) can be a great investment.

https://www.amazon.com/Crenova-Auto-Ranging-Multimeter-Measuring-Backlight/dp/B00KXX2OYY/

Haven't tried it, and it is extremely likely to be overcharged non-durable junk, but if it does work then I can't fault it!

If you want something cheap with a name on it, the Fluke 101 is decently budget friendly. Does everything my inhereted Fluke does, minus the current.