By fuel, they are referring to reaction mass. It's that stuff you propel out of the ship in the opposite direction of the one you want to go in.
The EM Drive has nothing to do with how the electricity is generated anymore than your toaster does, though both need it to do their job.
We have many satellites that have power, mostly via solar, that have been decommissioned and deorbited because they were out of reaction mass, excluding the amount used to deorbit them. If you don't need reaction mass, that's no longer an issue.
In conventional space drive technology, you have two basic types.
One burns fuel, which becomes a hot and expansive gas that then rushes out the thrust nozzles and provides thrust in the opposite direction. It doesn't matter if it was solid or liquid before it was burned.
The other is the Ion drive, which uses electricity to ionize a reaction mass and that then shoots out the thrust nozzle and you get thrust just like the other one. The real difference is the reaction mass isn't itself burned, rather it's ionized. So it's still pretty similar.
In both cases, you have a finite amount of reaction mass, which must be expelled to provide thrust, and before it's expelled you have to use more of it just to cart around the amount that isn't yet expelled.
Think of it this way, you have an electric cart that when it's carrying nothing but itself and it's one battery, it can go 20 feet before running out of power. Well, you can't go back for more batteries after you start out, so if you want to go further, you will need to carry the extra batteries with you. Let's say you want to go 310 feet. Well, that would take a total of 16 batteries, but it's also massively increased the weight of the cart, so one battery will no longer propel it 20', but only 12'. Well crud, now you need more batteries, but that adds more weight, and of course, the need for more batteries.
Do you see the dilemma here?
Sure, we have a small advantage, that if we travel slower, we use less power, but there are limits to that other than human lifespans and patience, both of which are relatively short.
That's part of why a reactionless drive is so fantastic. It doesn't have to conserve reaction mass, so it they can do a space version of petal to the metal as much as they want, so long as they don't screw the approach vectors. Travelling with short bursts of small thrust become obsolete as you can leadfoot it like crazy, and no space cops to bust you for going over the limit. So instead of a 3000lb probe of which 2800lbs is reaction mass with only 200lb for instrumentation, you know can have an 800lb probe with maybe 600lb of instrumentation. And even better yet, it doesn't even have to be a one way trip. As long as the hardware holds out, it can come home, or even divert to other points of interest. No longer having to rely on a reaction mass is a HUGE deal.