This is exactly what fennecfoxen just explained as to why you can’t just use one long trust and leave it at that. It’s unclear whether they’re going to put the craft into a graveyard orbit (requiring this maneuver, sans a destination of “another orbital body”) or let it burn up, though (from the article at least).

Actually you can use one long thrust. What you can't do is use one short one. The Hohman transfer orbit assumes short high-thrust maneuvers because those are the most efficient. But if you are using long low-thrust maneuvers, as would be the case here, then one burn can suffice if it's long enough. (This is how, for example, ion engines work.)

Source: I used to work for NASA.

Is it because burning far away from the periapsis, it would change the altitude of the periapsis?

Yeah, pretty much, though the full story is a little bit more complicated than that.

The reason a single short burn won't do it is that whenever you stop burning you will always be in an orbit that will return you to the point where you stopped (assuming you don't actually collide with the body you're orbiting of course). So you have to burn somewhere other than the orbit you want to get out of. The most efficient place to do that second burn is at apoapsis because that's where you get the greatest reduction in kinetic energy for a given delta-V (because that's where your velocity is the highest and so the force of burn is applied over a greater distance). But if all you have is a low-thrust engine (e.g. an ion drive) you can maneuver with long burns. The math gets hairier though.

Cool, thanks for the explanation. Looks like all that Kerbal Space Program was useful after all. :)