No, you haven't just found yourself in a weird Planet of the Apes remix. "Space monkey" is our narrator's term for someone who does "the little job [they're] trained to do" (1.10). Yeah, that's not a compliment.
At first, he seems to be talking about your typical corporate drone, like our narrator himself. These monkeys mindlessly plug away at their job, pushing buttons, performing tasks, and all for a small reward at the end: a paycheck. If their spaceship explodes (or their Twinkie factory shuts down), so what? There will always be another to replace them.
Eventually, though, this term evolves to describe the men who give their lives to Project Mayhem. When Project Mayhem fires up, the Paper Street house is filled with them:
A team of space monkeys cooks meals all day, and all day, teams of space monkeys are eating out of the plastic bowls they brought with them. (17.57)
The men seem to be filled with a renewed purpose in life. But is this any different than before? They're still working menial jobs and doing exactly what they're told to do. The only difference? Instead of working for a paycheck, they're working for Tyler. What do you think: is this an upgrade?
There's one particular space monkey who's way more philosophical than a nameless character ought to be. We're talking about that mechanic who takes our narrator on a dangerous joy ride through town. This guy is the Friedrich Nietzsche of Project Mayhem, expounding on the existence of God and the narrator's relationship to the big man in the sky. We can't do his speech justice here, so you'll just have to read it for yourself in Chapter 18.
You might notice that it's not necessarily what he says that matters. What matters is that he's a mechanic who has some serious philosophical thoughts. At one point, Tyler laments that "the strongest and the smartest men who have ever lived [...] are pumping gas and waiting tables" (19.12). Just because a man is a mechanic or a doorman (another nameless character who philosophizes at our narrator), doesn't mean he doesn't have something powerful to say.