The Death Star is 160 km across, or 80 km radius. It is a mixture of air and metal and other substances.
If we assume it is roughly as dense as water (as it looks roughly as dense as a ocean going ship, which is roughly as dense as water), it weighs roughly 2 * 10^18 kg. (If it was solid iron it would be only 8x denser, so this probably isn't off by more than an order of magnitude)
Earth weighs 6 * 10^24 kg and has a roughly 6400 km radius.
Thus the Death Star has a surface gravity of (1/3 * 10^-6)/(80 km / 6400 km)^2, or 0.2% of Earth's gravity. That isn't bad. But it has an escape velocity of roughly 60 meters/second (or 220 km/h or 140 miles/hour).
So if you throw a baseball out into the vacuum, it will fall back and land somewhere else on the death star, even if you are a professional pitcher. At the same time, falling 3 meters will take about 20 seconds, so it will "act like" zero gravity (ignoring any gravity generators).
Simply shoving something out an airlock will result in in falling back towards the death star somewhere else. If you spew vaporized trash out a nozzle, you have to eject it quite fast to prevent the slower particles from falling back on the death star. And nobody wants a death star covered in a thin layer of waste. Ew.
By compacting trash, you can launch it out of the gravity well with far less hassle and mess. And simply getting it to the surface of the death star will be a pain; compacted trash will be easier move around than loose piles.
Remember, vaporized things don't just "go away". That is only true in an environment where the environment picks up your slack and recycles things for you. The Death Star is a constructed environment, and doesn't have an ecosystem to clean up after whatever mess you leave behind (at least, you hope it doesn't). The creature in the compactor might even be there on purpose to digest some of the waste and turn it into something easier to handle, or might be a parasite. At least it isn't rats.
So: Compacted trash is easier to move around (over the 160 km interior). You cannot just open a door and throw the trash out into vacuum -- you have to launch it, either in a special purpose accelerator or in a special purpose garbage scow.
In both such cases, compact trash that doesn't fall apart is going to be easier to work with, and easier to temporary store, than either hot non-uniform plasma/gas or random piles of garbage.