Nier: Automata got me into music with made up languages. Though this pre-dates Nier, Yoko Kanno and her alter ego Gabrielle Robin made a song called "Moon" from the Lodoss War anime series. Pure fuckin Gold
Twisted Metal 4 had great music. I junior high I ripped the tracks and burned a copy so that I could listen to the soundtrack on my way to school. I recently looked up the soundtrack on YouTube and discovered several of the songs included in the game as instrumentals actually had vocals, and some of them were edited in other ways to better suit the theme of the game. I've found the original versions are better, and some of the artists have great catalogs.
Cirrus - Time is Running Out
One Minute Silence - And Some Ya Lose
One Minute Silence - A More Violent Approach
Ghoulspoon - Alien Magnet
Tony Hawk's Pro Skater always had good music, but the best song in the series is definitely this one:
Three Inches of Blood - Deadly Sinners
And I can't leave out the best song to ever be included in a video game:
Fallout, 100%. I loved listening to the old world shit, and I was always a fan of the Blues, so it reminded me of what my dad used to play over the radio when I was a kid. It was so interesting to hear music like that.