For those who'd like a slowed-down version to see what's going on without running in the emulator:
This TAS completes the F-Zero X Death Race as quickly as possible, with a time of 5.866s. This improves the prior published TAS time of 8.927 by Katsukawa Sojuro aka Xenos (Xenos reports an unpublished time of 6.993s by throwing the car off the side as this TAS does).
The unassisted world-record is 24.745s by Daniel, played in PAL (20.621s converted to NTSC). There's no video of that time, but this video [dead link removed] by the same author is almost as fast.
I used Mupen64 0.5 re-recording v8, with "Memory Hacking Software" to find and view memory addresses. For information about the game and some of its techniques see my Jack-Cup TAS comments.

Goal Choice

The Death Race is a standalone challenge within F-Zero X, so a standalone movie seemed the only way to present it. The goal is simple: destroy the other 29 ships as quickly as possible, aiming for in-game time.
This movie choice has been brought up in the forums a couple of times, but never really drew direct commentary either way since 2007. In my view, though, this movie demonstrates feats clearly only possible with TAS (destroying on average 4.9 cars per second; 5.1 if you include the player's car). For comparison, the unassisted world-record is 24.745 (played on PAL but time adjusted to NTSC).

Damage-Boosting

One key technique is to boost off dead ships by crashing into them at the right angle after they bounce off a wall. This can be quite tricky as you don't get the boost if you're in the middle of a side-attack (aka DT-R or DT-L) when the ships collide, and essentially all steering uses side-attacks (it's the only way to turn quickly enough). Finally, both the rotation and relative position of the colliding ships affects the path the destroyed ship will take; the closing speed of the collision affects how fast the destroyed ship will careen away - so all of those factors have to be controlled for to arrange the optimal boost.

Enemy Manipulation

I tried to preserve the ships in their original line-ups and swing through them for maximum efficiency. When ships would get out of position I'd try to use other ships to adjust them, using the same techniques used in setting up damage-boosts. This was very meticulously done in setting up the "endgame", where the lead ship was forced to slow down by hitting a dead car, and then killed simultaneously with another ship. At that point I slow down as fast as possible and kill the remaining 4 ships, which I'd managed to bunch together very tightly, at the same time generating speed to fly off the edge and stop the timer.

Car Choice

The movement of the first two cars destroyed seems driven entirely by which ship you choose. There are only 3 or 4 patterns; Golden Fox gives the best pattern where both cars break immediately to the middle. Crazy Bear, Mighty Hurricane and Great Star (heavier high boost cars) give bad patterns. Also, GF is heavy enough to kill easily, and lighter weight = faster steering - obviously important for this challenge!

Misc

I use the wide-angle view because it's easier (for me and viewers) to see what's going on. And quite a bit is going on - ships get flung everywhere when they die and can interact with both the player and other ships, making planning, patience and experimentation crucial.
Finally, you can save a couple of seconds by throwing the car off the side at the end, which stops the timer earlier.

feos: Cool run, great feedback. Accepting to Moons. And publishing.