When he says a demand for dollars what he means is more of a demand for savings. Its a demand to hang on to cash as opposed to spending or even investing.
One of the reasons that the FED has the ability to print seemingly without repercussions is that the dollar is the world’s major reserve currency. Its the currency that other nations hold in there central banks sort of as the basis of their currency. In the past this would have been the place of gold. I am not sure of all the details about this and I am sure Prof. Herbener can explain this much better. Suffice to say, as long as the central banks of other nations want to hold dollars in reserve in their bank, the FED can keep printing because the dollar will stay in demand.
If one currency becomes more stable than the devaluing mess the FED has created, countries may start switching over to that currency. Then the demand for dollars would start to drop fast and we would have the inflation problem that you are expecting to see. In short, this part of the puzzle will continue as long as other nations see the dollar as the most stable currency. I am sure this isnt the whole story but I also cant see how it wouldnt at least play a part.