I think that the evaporation in theory is able to cool the room, the heat energy is transferred into launching a bunch of water molecules airborne so to speak. Hanging some wet towels around would also do that.
However, the performance of such small devices is probably not sufficient to significantly cool a room, and it has a lot of drawbacks (filter gets mouldy easily, ...)
Here's an excellent video about these swamp coolers: https://youtu.be/2horH-IeurA (he has many videos on heat pumps and stuff)
Oops, thanks for noticing :) updated the title.