Well, he may not know much about Islam. I don't either. But even the page you linked quotes:

"Fight those who believe not in Allah nor the Last Day, nor hold that forbidden which hath been forbidden by Allah and His Messenger, nor acknowledge the religion of Truth, (even if they are) of the People of the Book, until they pay the jizya with willing submission, and feel themselves subdued."

"Jesus will come again, and at that time will (among other things) abolish jizya, will "perish all religions except Islam""

Which I would translate to simple words as: slaughter those who are different, unless they pay you. If they do, whoever is accepted as Jesus can slaughter them later anyway. In modern world that's protection racket.

PS, While it sounds harsh, that's how I understand it. If that's not the right idea, please do explain it better.

The point is that this system, while penalizing non-muslims, allowed a mostly peaceful coexistence between different belief systems in the Islamic world, thus demonstrating by example that the notion of Islam not being compatible with other religions is wrong. On the other hand, the tolerance track record of, say, the Catholic Church was fairly dismal until its influence over politics became dramatically curtailed.

Honestly, I don't think I can accept that as a "peaceful" solution. Same as mafia can't be described as peaceful when asking for money not to destroy your business.

Simple test - any other religion with the same rule wouldn't be able to coexist peacefully. It's just luck that we have only one.