Why does the PSP version of Higurashi Daybreak have an entry on speedrun.com but not the original on PC? Am I allowed to speedrun the PC version of Higurashi Daybreak Kai? I don't understand.

unfortunately this leaderboard includes ONLY the Higurashi Daybreak Portable version. If you want to make runs on the PC version, you have to request the Game by yourself (speedrun.com > Games > Request Game).

As MrPleb said, you have to request the PC version of the game yourself, as it is different from the portable version. However, if you want to speedrun the portable version, all the resources are there. Just go to the resources tab of this speedrun page. The link to the ISO is there, and you can use an emulator such as PPSSPP which works great.