This idea has been around for most of the 20th century so nothing new or even clever about it.
Popular mechanics ran a story about doing it then quickly retracted the story in the following issue after the dangers were made apparent to the people who have no fundamential understanding of how 4 cycle engines work.
Decades ago a similar device was marketed for 4 WD adventure touring.
It replaced a spark plug.
Finally it got banned after dozens of people died using it.
Some emergency vehicles still use them and as a last ditch get you out of a potential death situation they are OK but not & never will be a replacement for a proper compressor.
Considering you can buy 12 plug in compressors for under $ 10 why bother with some thing like this.
It will cost more to make than buying a small 12V plug in.
I have a 1/2 dozen battery starter packs with a built in compressor . a far more useful device than this trash.
Despite the charcoal filter the bulk of the fuel will pass into whatever you are inflating effectively making it a bomb.
Remember that on compression stroke you are pumping unburned air/fuel mixture into your tyre
Then on the following power stroke you are pumping the burning fuel air mix then plain exhaust into your tyre.
Exhaust is very hot so the whole shebang will get to very near muffler temperature so there is a burn potential.
Exhaust gas pressure is in the order of 1400 psi so the system would get a 100-140 psi charge from the compression followed by a 1400 psi pressure pulse from the combustion.
The poster is an idiot moron fool and is encouraging others to risk serious injury for absolutely no benefit.
Even making a compressor by converting an old engine into a pump and powering it with another engine does not work particularly well and there are thousands of videos about how to do that.
Compressed air is very dangerous , in fact compresses any gas is dangerous and fooling around with some thing that your do not understand is a sure fire way to spend a holiday laying on your back in the ICU ward of your local hospital.