Upvote:1
No. Game of Thrones is a fantasy series, loosely based on medieval and renaissance history. This is an example of fantasy. I've searched for unusual trebuchet types, and came up blank. All I found were common trebuchets.
There's a good reason for that: technology wasn't advanced enough for this kind of trebuchet. It needs guiding rails and pretty smooth ball bearings to overcome friction. Modern ball-bearings were invented in 1794. They wouldn't be good enough to work on a machine like that. You'd need much better bearings. No idea how accurate, but you'd be thinking at least a century later.
A trebuchet works like a giant sling. The longer the arm, and/or the heavier the counterweight, the further it would reach. It's fairly easy to construct, at least in theory.
The trebuchet you're interested in wouldn't be half as efficient as the common one. A shorter arm, shorter travel time and very complex construction. Likely it might fall apart when it reaches its apogee. The forces it has to withstand are huge. The technology and available materials that can tolerate that kind of stress hadn't been invented yet. Medieval tread mills for example were very dangerous. Many of them broke under stress, with disastrous consequences for those around it.
An other point to consider is what that trebuchet is used for. It looks like a very early form of air defense, which is preposterous to say the least. You could hit the wall of a castle with it, and that required some training plus trial and error. Castles usually don't move a lot. Trying to hit something that moved was simply not possible.