WOW!!
What you're seeing there is the sign of a true pro. Eddie (apparently) either can't hear his guitar or can't hear the synth and is just playing what he always plays even though it's not in the same key as the synth.
From what I've heard of them, could he have been too stoned out of his mind to realize?
About all I know of their catalog is that song and mention of Eddie van Halen in regards to guitar techniques, not a band I follow. It's just that I know that most musicians I know of would have just stopped, said "Okay, F that, next song is..." and launched into something else if there was a failure of equipment.
On-stage hell for the performers, definitely.
One might hope that enough such incidents might bring back live performances ... but I won't live that long.
One of the best concerts I ever attended (many years ago) was a John Denver concert. He had played two other cities in the two nights previous, it was winter and lousy weather, and the guy was obviously and visibly tired and suffering. But he sang. He didn't lip-synch, he SANG. There were several places during the night when his voice cracked, but he SANG.
Ya know, the voice cracking didn't detract from the performance one iota, because even with the vocal flaws, you could still feel how he felt about what he was singing. Lip-synching doesn't convey any emotion whatsoever.