You could argue Green Room is more of a thriller than horror, but bones are broken, throats are ripped out, people are shot in the face, and the camera rarely cuts away to spare us the gruesome imagery. At that point you've departed the realm of the thriller. There's no supernatural element—not that that's a requisite for horror—but the bad guys here are definitely monsters.
So a punk band are hard up for paying gigs. Reluctantly, they end up playing a rundown neo-Nazi joint in the middle of nowhere. In true punk fashion, the band decides to piss off the skinhead crowd by opening with a cover of the Dead Kennedys' "Nazi Punks Fuck Off." That goes over about as well as you would imagine. Fortunately, the rest of their set is hard enough to win the assholes over and the band members aren't murdered onstage.
After the show the band heads back to the green room to discover their equipment has been set in the hallway backstage. They're told the headliner has arrived and they needed the room. So our heroes are on their way out when one of them realizes she left her phone in the room. When they return to fetch it, they discover the real reason they've been kicked out: a young woman is lying on the floor of the green room with a knife sticking out of her skull and the venue's operators are scrambling to cover it up.
The band gets so far as calling 911 before their phone's confiscated and they're locked in the room with a big psychopath who's armed with a revolver. He subtly mentions the gun only holds five cartridges, "because they're so fucking big that's all that can fit in the cylinder." Meanwhile, the bad guys outside the room call the venue's owner, who happens to be the leader of the local skinhead gang. He's played by Patrick Stewart whose performance is neither too little or too much for the tone established so far, further proof he's one of the best actors alive. He just wants to get the kids off his property as quickly as possible. Little do they know it's so he can murder them elsewhere and stage the scene in such a way it makes it look like they got themselves killed for trespassing on another piece of land.
So, as crime movies are wont to do, a simple premise becomes complicated rather quickly. Patrick Stewart, who's trying his best to keep the situation from escalating, comes up with one idea after another to flush the kids out. The kids have to do everything in their power to keep the skinheads from getting in and they're only somewhat successful some of the time. What's interesting is Stewart's character is paying people to deal with the problem so matter-of-factly, he might as well be coordinating the extermination of rodents. To him, it's just another problem in the life of a businessman—albeit an amoral one who happens to be the leader of the local skinhead group. Another interesting choice is the skinheads aren't caricatures. When Stewart loses his cool and humiliates one, he genuinely apologizes. The biggest reason Stewart's having so much trouble getting the kids out is his henchmen aren't expendable in his mind, they're family and he cares about each of them. He doesn't want to send them into harm's way.
If you need a lot of fantasy in your genre flicks, and main characters who do incredibly heroic things, make the right decisions at all times, and never take a lickin', then this isn't your movie. We all hate movies in which stupidly written characters do stupid things, but here's a rare example in which well-written characters do stupid things for good reasons. The reasons are they're young, immature, and panicking. You'll only yell at the screen in frustration if you're one of those armchair tough guys who think you'd suddenly become John McClane when put in a similar situation.