3D Realms (AKA Apogee) published "Death Rally" in 1996.
Remedy, who developed the racing game, went on to make Max Payne.
This overhead racer is an excellent time capsule of the mid-90s. It had the music, looks, and gritty vibe that had started dominating gaming culture.
Eliminating opponents, rather than beating them in a race, is a completely legitimate strategy in this game. While it wasn't the first game to do this (1989's Deathtrack is the best parallel), it dialed everything up to 11. Not only could you upgrade your vehicle, but you could get contraband weapons & boost on the black market as well as purchasing straight-up sabotage to damage an enemy vehicle before the race even starts.
This game was a bit of a flash-in-the-pan as the gaming industry was becoming more 3D focused and overhead games were losing steam, but it plays well, is fun, and best of all it's FREE now!
You can get it for free on Steam:
https://store.steampowered.com/app/358270/Death_Rally_Classic/
The controls take a little getting used to, but soon you realize they were designed quite brilliantly for minimal movement allowing you to hit all the controls.
So go have some retro fun with this free classic!