MacBook Air 13 Inch(Early 2015) Shuts down while playing a game?

So just a background and idk if this is part of the problem but it could be, my MacBook Air won't turn on without being plugged in. Basically I have a problem with my laptops battery and it needs to be charged at all times or else it will shut off.

Now that bit of information is out, my PROBLEM is that it now keeps shutting off whenever I play a game like RuneScape. I've played games on this laptop before with much higher requirements like WoW and it never gave me any problems and during those times, my battery was already bad and my laptop had to be plugged in at all times.

I wanna keep an open mind so I want look for several solutions to my problem before I go to the store and have my battery replaced (if that's whats causing this problem).

Once I start playing runescape or other games, after a few seconds of logging in, my laptop shuts off completely. I can turn it back on with no problem but It still has the problem of it shutting off once I start to play a game.

Any solutions would be helpful please before I think about replacing my battery.

MacBook Air 13 Inch early 2015 model

OS Big Sur