Is it legal to make your own Mario video parody?

Answer 1

Parody is one of the uses considered to be fair in many countries; however, court rulings on fair use are inconsistent. If you have concerns, it may be worth your while to contact an experienced copyright lawyer.

Answer 2

Unless you have permission from the game's copyright holder, it's technically probably a violation of copyright. You'd have to have a compelling "fair use" exception to the copyright protection for it to be, strictly speaking, legal.