“This isn't fun anymore.”
Stop the game. Put it on pause. Say "I'm stopping the game. Let's pause here. We need to talk."
You have a player who is unable or refusing to play according to the general agreement of how the group will play. Put that on the table without accusation. "We're trying to play a game together here, and that means we all need to cooperate. This isn't fun anymore, because we're not cooperating." You don't need to accuse him, you don't need to say that he is making the game un-fun. Just that the game isn't fun anymore.
“How can we start having fun again?”
Put this out there as an honest question. How can you all work together to have a game that everyone can have fun with? You have one player who seems to be saying that they need to be in the spotlight all the time to have fun. Enjoying the spotlight is a legitimate motivation for playing roleplaying games, called "Expression" in one taxonomy of game motivations. To solve this with this player's cooperation, you have to go into the conversation knowing that their underlying, fundamental reason for doing these things is, on its own, perfectly OK.
You need that, because to figure out how to fit them into the game hinges on figuring out how to satisfy their creative motivation without it taking the game away from the other players. Right now, the player is trying to figure this out on his own, and failing to do it. Your job, and the job of the other players, is to help him figure out how to get what he wants out of the game in a way that also gives the other players and you what they want out of the game.
At this point, it should be obvious to everyone that the game is not continuing until this puzzle is sorted out. If it's not obvious to everyone, this is the time to say it in so many words: "This is a puzzle we need to solve as a group. We can't play again until we do."
I don't know what you're conversation will turn up, so at this point I'm speculating, but if my guesses are near the target, they might be useful to you. So, continuing...
Sharing the spotlight
You've got a bunch of neurotypical players and one player who might be on the Asperger's-Autism spectrum. Okay, that just means you need to change how you communicate. You can't leave it to him to know when he's crossing a social boundary, because you're all communicating the transgression with a mix of words, body language, voice tone, implication, and the majority of that stuff just doesn't register with him—to pick up on the social dimensions of your communication that This Is Not Okay he probably needs to use super-focused concentration. That's not something he's going to be doing at all while he's also focused on the shared imaginary space that you're all creating together. You need to put all of the relevant information you need to communicate into the actual words you use, and only into the words.
You need a Batsignal. You need a codified signal that you can use to indicate that now is not his spotlight time—so that it can shine on another player, so that everyone has their turn. To get that Batsignal, you have to have a conversation about how everyone needs spotlight time, and spotlight time will often be alone time. He wants to be in the spotlight—make it clear that he can only get spotlight time if the game is happening, and the game will only restart and continue if everyone's turn to stand alone in the spotlight will be respected by everyone else who is taking their turn out of the spotlight.
Your Batsignal can be as straightforward as saying that it's not his spotlight time: "John," (I'm going to call him John for a minute) "this isn't your spotlight moment, it's Mary's. Her thief is going to do her cool thing right now, and we'll get back to you in a minute. OK?" If he acts like he understands, continue with the action with whatever he said his character was doing to jump into the spotlight didn't happen. He might jump in with another declaration, at which point you repeat that "this isn't your spotlight moment, we'll get back to what Johnivisus the Shining is doing after this," and continue with Mary's spotlight moment.
Whatever your Batsignal is, it has to be something that is completely contained within the words you use. It has to be something he agrees to. It has to be short and unambiguous. And you have to enforce it by ignoring the contribution he made that resulted in you turning on the Batsignal.
This is a Block, to use a term from improv. Lots of people instinctively recoil from the idea of so bluntly denying someone's contribution to a creative endeavor. You probably will. It's not something you'd normally do... and that's why his choices are causing problems, because he's not operating how the group normally does, and your normal response rests on the assumption that he's playing the same way y'all are. Predictably, your inappropriate response to his actions produces an outcome that is undesirable.
So, the block is necessary: you have to gatekeep the shared imaginary space a little bit more than you otherwise would like to, in order to manage a table-level communication mismatch. This is necessary, because communicating effectively is the only way to functionally share the imaginary space, to play nice with each other's toys. Fixing the table-level communication before implementing the communications into the game is necessary.
Let him be awesome
The flipside is that, to get him to be OK releasing the spotlight, you have to make sure to shine the spotlight on his character too. You have to hold up your end of the social contract you're making, by showing him that he can have spotlight time without grabbing it away from another player.
But maybe it's not Asperger's? Batsignal anyway!
This is all written in the context of taking your guess about his neurology and communication style at face value, but the advice is actually the same without that assumption: fix the communication at the table-level before trying to continue to play the imaginary game. The very fabric of the game is accurate communication, and for it to exist and for you to play it, fixing the communication is necessary. It doesn't really matter why the breakdown is occurring, and these conversations I'm advising you to have are a necessary process to fix it.
Stopping the game, solving the puzzle of not-fun, and implementing that solution will help regardless of why this player is making these choices. It might not be the complete solution, it might uncover other issues, but then it's even more a necessary first step. And, it will give you all some useful practice in solving group-level problems as a group, outside of the game, so that you can tackle the next puzzle effectively, together.