Why are some games np-complete?
It just means that you can create levels or puzzles within these games that encode NP-Hard problems. You can take a graph coloring problem, create an associated Super Mario Bros. level, and that level is beatable if and only if the graph is 3-colorable.

If you want to see the specific way the NP-Complete problems are translated into the games, I recommend the paper "Classic Nintendo Games are (Computationally) Hard". It's well written and easy to follow.

An important caveat to keep in mind is that the NP-hardness requires generalizing the games in "obvious" ways. For example, Tetris normally has a fixed size board but the hardness proof requires the game to allow arbitrarily large boards. Another example is off-screen enemies in Super Mario Bros: the proof is for a variant of the game where off-screen enemies continue moving as if they were onscreen, instead of ceasing to exist and being reset to their starting position when Mario comes back.