Ok, forget the compressor, with that sort of sound compression is superfluous - especially as the limiter on the quilter does essentially the same thing.
You need masses of gain, on the amp and on the pedal. Consider investing in some cheap pedals (e.g. Behringer Tube Overdrive a tube screamer clone) or maybe a fuzz or distortion pedal rather than just overdrive. There is delay or chorus in there too, as a minimum use some of the amp's reverb. Once you are close to the sound you want, you might upgrade, or feel you don't need to.
Bad news is that Yngwie uses stacked humbuckers in his guitars, tele PUPs are pretty weedy single coils that give the classic thin, biting sound, even more than a Strat. That's one reason why they aren't popular with shredders.
Best thing to do is dial gain and tone controls (especially the mid range) to max, then back things off to get the sound you like. You don't get a sound like that by pussyfooting around.
If you can't hammer on a note and get a creamy distorted sound you won't get anywhere near that video.