Like Cari says, it's an old game. Google "8 bit Mario". "8 bit" refers to early computers that transferred (for lack of a better word) data 8 bits at a time. Most desktop and laptop computers are now 64 bits. Images back then were jagged and slow moving. From the images on Google, you could develop a pattern easily. Mario is the name of the character in the game. I think they are still making Mario games, but they are much smoother and faster moving characters if they are.
I don't envy you making this quilt. It's going to be a lot of little squares, unless you decide to make one big "Mario". I never played the game, so can't help you with which characters are/were popular. Ask Cari, she might remember. Or, do a new post on Mario characters. Maybe someone played the game or a family member did that they could ask.
I found this google tab that shows some characters "pixilated", which is what they are looking for in an 8 bit Mario image:
https://www.google.com/search?tbm=isch&q=8+bit+mario&chips=q:8+bit+mario,g_14
ixel+grid&sa=X&ved=0ahUKEwigq5LLmObVAhWIJCYKHQGODsAQ4lYIQygA&biw=1600&bih=767&dpr=1
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