What exactly did Jimi Hendrix do, technically, that separated him from his rivals?

Well let me know which one of his rivals was doing these things:

Opening up the Monterey Pop Festival with a rendition of Killing Floor that was twice as fast as the original:

https://www.youtube.com/watch?v=2ARliZIZDhg

^ this is the not the actual performance but it can be seen in the Live at Monterey DVD

Setting his guitar on fire at the end of Wild Thing:

https://www.youtube.com/watch?v=_-7toYWFEyk

playing the guitar with his teeth and behind the head

https://www.youtube.com/watch?v=CiR36mDzqVI

Using Octave Doublers like the Octavia on songs like Fire

https://www.youtube.com/watch?v=OJV3EYto6II

Creating psychedelic dreamscapes with songs like 1983..

https://www.youtube.com/watch?v=OlgOHLHziJ4

Recreating scenes of war and bloodshed with songs like Machine Gun…

https://www.youtube.com/watch?v=hvv–UkFfV8

Simultaneously playing lead and rhythm on songs like Little Wing

https://www.youtube.com/watch?v=BkEPBiMbgxs

Very unconventional chords and phrasing on songs like Angel

https://www.youtube.com/watch?v=HBrO1TcZLLQ

… and did I mention doing all this while high on acid too?

That’s why no other contemporary could match up with Hendrix it’s not just his technical ability and skill it was his showmanship, his creativity, his range, his raw emotion etc everything combined together. It’s like with Bruce Lee. There’s a lot of modern martial artists who technically was as good as Bruce Lee or even better – but they aren’t Bruce Lee. He was the original, the innovator, and when you watch his films you can see the raw-ness of his emotion. It’s same with Hendrix, even decades later sure you have guys who can technically run circles around Hendrix, but they aren’t Hendrix, they are lacking the creativity and emotional aspect.