Most of the browser games on itch.io require very little resources. It won't be your PC or Windows version.
I just tried 4 browser games on Firefox and they all worked (two of mine, and two written by other people).
There might be a problem with the specific games you were trying to play - they could be crashing on start-up.
If you have the issue on a game you could previously play, then you could try to delete your browsing history from Firefox. If it's only allocated x amount of space and that space is used up, you might struggle to open anything else in Firefox.