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I can't watch the vid due to being at work, but have you checked the TPS, could need adjusting/cleaning. The only other thing, which is weird that I have seen cause something like this was infact the pickup tube for the fuel pump, the rubber connection from the pump to the hardline inside the tank had come loose enough to not allow enough fuel when throttle was applied. Good luck!

 

Fuel filter might be clogged, try taking it off and blowing through it

 

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does it cut out at lower rpm's if you full on throttle it. Or just when it gets up to 3500 or so?

 

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Can you hear the fuel pump relay actuating when you give it gas? It is behind the passenger side kick panel. I just dealt with this same problem with my 4runner except it didn't cut out until about 1500 rpm's. I would start by checking the codes, and depending on what that tells you, do a resistance test on your tps, it's very easy. My problem was a dirty tps. The spring wasn't returning the sensor back to the closed position. Cleaned it and works great.

 

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