Can I use a higher wattage charger than my laptop requires if it doesn't charge when I'm doing demanding things like playing games?

If you think your Mac's battery is not charging properly, read My battery isn't charging.

Make sure you're using the correct power adapter and cable for your Mac. The ones that came with it ought to be sufficient, and a larger capacity one probably won't help. It certainly wouldn't hurt anything to use a higher capacity power adapter but it won't charge any faster with one. A Mac will draw the lesser of whatever power the adapter and cable can provide or whatever the Mac requires.

Please read Find the right power adapter and cable for your Mac.

Then, keep them clean and cool:

Keep your Mac notebook within acceptable operating temperatures

If your USB-C power adapter isn't charging your Mac notebook

Apple Portables: Troubleshooting power adapters

Yes, you can, if you can find one that works with your computer. But it is not necessary. The battery continues to charge, albeit slowly. Furthermore, if the charger is connected while playing a game, then you aren't using the battery unless the game demands more power than the charger can provide. That is not likely going to happen except infrequently.

Did you read the information at the link provided by John Galt in his post above? It clearly thates in the first paragraph:

"You can use a compatible higher wattage power adapter without issue, but it won't make your computer charge faster or operate differently."

Schopski wrote:

The game is demanding more power than the cord is providing. Will a higher wattage charger solve this issue without harming my Mac or battery?

The distinction between charger and cable (or cord) is significant. Either one can limit the power supplied to your Mac, but neither one will result in any harm.

Read the Apple Support documents above, particularly the passage beneath Make sure you're using the correct USB-C charge cable.