That's true in and of itself, but there's another aspect to it too. While fasting is traditionally associated with giving up food, it isn't limited to that. One can "fast" from the internet, for example, or from sex with your spouse (by mutual consent and only for a time, per Paul), or from anything else that brings pleasure to the flesh.
In many cases, serious demonization is associated with some specific sin, and until the person is willing to break all ties with that sin, the demons can't be removed. "Fasting" in this case may refer to that kind of giving something pleasurable up that is a gateway.
Let me give a personal example: I happened to love comic books as a kid (and still do, though I don't actively collect). Unfortunately, because in many cases I bought certain comics solely because I wanted to see the babes in spandex (gimme a break, I was in my teens), they became a gateway. It was revealed to me the other night that I need to make a clean break from those comics and toss them out, and I'm in the process of getting rid of the problem books (I may end up just tossing out the whole collection).
Now, I'm not saying that comic books are evil or satanic or that nobody should collect Superman if they enjoy it. What I'm saying is that in my case they were a gateway, so I'm "fasting" from them in order to seal off a door. For another person, comics might not be a problem, but idolizing a sports hero, something that has no draw for me, might be (just for example). In that case, he may need to "fast" from that sport for a time or permanently, while I could continue to watch and/or participate to my enjoyment.
The particulars are not set in stone. It's a matter of being willing to give up certain things that have a hold on you for God.
agreed