Translation:We are not stepping into the room, but into the dining room.
I think, in this context, this "room" is closer to the living room. If we just finished dinner in the dining room, or in the kitchen, but keep sitting around the table, someone might say, "okay guys, let's go to the.... ". And Hungarian would frequently say "... a szobába". That is, out of this functional place and back into the room where we can hang around comfortably. The sitting room, the living room. A bedroom is also a "szoba", but the first association is the living room.
I'm no expert, but as far as I know the ba/be ending implies movement- into, whilst the ban/ben ending simply means- in, without giving the idea of movement. Somebody tell me if I'm wrong, please :-) There are probably also some idiomatic uses of these endings, which are exceptions to the rule.
You are right, -ba/-be are the directional ones, -ban/-ben would mean walking around inside the room.
(About the idiomatic use: in slang and in some regions people often only use -ba/-be, ommitting the -n in either use cases. So you could hear it that way, but probably don't want to learn it that way.)