How does the word tetra relate to the game Tettis

First off do you mean the game tetris? If so here is the answer:

Tetra is a prefix which means "four" and is used when forming compound words. In tetris, we use pieces (called tetrominos), which are formed by combining 4 small blocks (called minos). There are 7 possible types of tetrominos named after the letters that they resemble: I, O, L, J, T, S, and Z.