Does anyone know of a good pixel-like, retro video game font that is web-safe? I am having trouble finding one.
Unfortunately, none of the "true" web-safe fonts really fit your description (W3Schools has compiled a useful list of safe options: W3Schools page on web-safe fonts).
What you could do is use the @font-face rule, it's widely supported nowadays and pretty easy to implement: http://www.w3schools.com/cssref/css3_pr_font-face_rule.asp
My favourite old school game font is Arcade Classic, you can get it here: http://www.dafont.com/arcade-classic-pizz.font