I've seen nothing, including that video, that would lead me to conclude anything other than the F-22 is the finest air to air fighter in the world, in pretty much every category and situation.
The closest comparison I can come up with, regarding F-22 vs. Rafale, is my experiences flying the F-15E vs. the F-16. When in a "fair" fight starting BVR, the F-16s had great ideas plans and tactics to get close enough to force a visual engagement, but they never really expected to get to the merge if we didn't make a pretty big mistake. Nothing against the F-16 at that point, but the F-15E has more missiles and a significantly better radar. And there are other F-15 specific systems that gave the Eagle an advantage, BVR. We had to foul up to lose, basically.
Even then, if we did have to go to the merge, we have tactics designed to ensure that an Eagle wouldn't end up 1v1 against a viper, because it would likely lose. That said, on occasion a well flown eagle would surprise a poorly flown viper and get a BFM kill, even 1v1.
For that video, I suspect that the F-22 driver was having a bad day or as the unnamed source claims, it had some sort of configuration limitation. We'll never know, the hud video isn't really that clear. But I HAVE seen a well flown F-15C spank a reasonably well flown F-16 4 out of 5 tries, because at some point pilot skill really does play a huge part. Hell, for that matter, this one guy with 5000 hrs in an F-5 flying for the Bahraini Air Force gave us absolute fits even 2v1, because he was THAT GOOD and the environmentals (slightly hazy day) made his tiny plane disappear every time he pointed his nose at us. BVR he would have no chance, and on paper he should have little chance in BFM, but he was an outstanding pilot and took every advantage and as a new guy with 200 hrs in the plane I simply couldn't deal with it in a timely fashion. Yea we "won" in the sense that he couldn't kill either of us before he ran out of gas, but we couldn't kill him either, not within our training ROE anyhow.
Same goes for a C-130 I played with for an hour... He wanted to practice some defensive reactions, and his aircraft defensive systems and defensive maneuvering lowered the Pk on every one of my 8 missile shots. Then he went to 500' AGL and I couldn't gun him without violating low altitude training rules. So yea, a C-130 "won" the training BFM engagement against an F-15E. In RL, who knows. But he made every one of my missile shots unassessable or invalid in a training environment, and his maneuvering made it impossible to get a gun shot without violating one or more training rules.
Like the one time I, all alone, managed to bounce 11 F-16s who never saw me coming. I came in at 500' behind a ridgeline and did an immelman right into the middle of their formation. I popped one during the climb, but could only get tally on 11 of them. During the briefing I was told there would be 12 of them, so after the merge I was "trapped" in my altitude block, unable to maneuver to make further kills. I counted 11 bandits three more times before about 6 of them cleared off their missile rails at me
It turned out the 12th guy ground aborted and never took off, but I didn't know that so I was handcuffed by the training rules. So 1 eagle "beat" 11 F-16s at the merge by jumping them completely unaware, but they shot me to shreds due to a safety related training restriction.
The point is that we don't know why that rafale was able to maintain the offensive on the F-22 but what I know of all modern fighters tells me that the F-22 is superior in pretty much all areas. The Rafale and Eurofighter are both fine aircraft, don't get me wrong. But the F-22 has all that, plus stealth...
