Okay, the only thing I can attest to is the sound of the engines; they do sound like air turbines and not combustion engines, especially on landing when they are thrown into reverse (excuse my layman’s ignorance of proper terms) What did you think of the video? I cannot disprove anything they are saying.
The engines aren’t “thrown into reverse” ... “thrust reversers” deflect the exhaust forward to assist in braking.
If you’ve got a window seat abeam the engines you can see this yourself.
That's why you should familiarize yourself with the operation of turbojet and turbofan engines; do your research from multiple sources, not just the ones promoting this "air compression combine theory".
Do you know the differences among the following types of aircraft engines?
1) Turbojet
2) Turbofan
3) Tubosprop
Can you distinguish between a turboshaft engine and a free turbine engine (hint: two types of Turboprop)?
I'm going to guess that the answer is "No" and "No". And that's OK; its not your field of expertise. But you can get a non-professional's working understanding of these topics by your own research on the internet. Do that, and you'll be ready to address the problems with that video you linked for me.
"Wikipedia" is not a bad place to start.