I don't think you can have a Matchlock bolt action.
Is it really not possible though? I wonder if it could be made to work. I know it's all souped-up anime weaponry, but still.
A firelock mechanism would suggest the bolt ejection for casings might not be what we're seeing. It could just for accessing the chamber like an incredibly overdesigned trapdoor rifle. Maybe it's just like the liberator pistol and the "magazine" is just an empty box for holding paper cartridges that need to be taken out by hand. I can certainly see the appeal of a firelock weapon having a couple spare bullets on the gun itself, especially if it was water resistant.
However, while I'm not very familiar with matchlock designs, it doesn't seem like there is any kind of pan on that side, and it looks like the bolt is in the way of the match when it's down like that too.
here are my speculations on the "logic" of the design the bolt has a flash hole, the magazine probably has an integrated cut off so you dont go willy nilly make a chain fire, chances are it could be a breech loading match lock so the magazine should more or less have an elevator rather than a follower, there a lot of forgotten weapons designs all in one package
considering they might be using black powder cartridges and guess what the Mosin-Nagant was designed originally with black powder in mind so not that far fetch when it comes to "can the gun take the pressure"