Buy a digital clock!
Broken Chess Clock.

For a nice clock like that I wouldn't risk trying to mess with it myself. I would go to a watch repair shop. Many will give free or flat rate estimates. I would also invest in a cheaper digital clock for blitz and leave the nice clocks for slower time controls. Beautiful clock btw.

If you don't know what you are doing, don't touch it. It's a straightforward fix at a watch and clock repair shop

The winders unscrew in the opposite direction, i.e. you turn them anti-clockwise to wind up the clock and you have to turn them clockwise to unscrew them. Putting the minute hand back on is rather easy, as they are only attached and only have to be put back on and pressed tightly. The problem is that you need to pull out the clockwork for that, and in order to do so you need to remove the lever for the push buttons, as it is difficult to impossible loosening the upper two of the three screws that hold each clockwork (see pictures). Removing the lever can be done without any problems, but it is tedious fiddling.

Lol, I'm going to have to agree with @jjupiter6 on this one. Seriously, it might be a simple low cost fix, For a Professional , but messing around could turn it into a high cost repair.

An explanation with photos on how you can fix it is certainly helpful but may give you a false sense of expertise & quickly lead you to convince yourself to fix it until you make an irreversible mistake & realize you never had the skills or the right tools & shouldn’t have touched it.
The choice is yours
He broke it playing blitz, its not going to survive long anyway.

I totally agree with the comments above regarding EXTREME caution! You could easily mess things up good and proper, and end up paying a LOT more to have it fixed.
That said, there's no harm in opening up the back and having a look, as long as you can resist the urge to tinker with stuff you know nothing about, right?
I recently purchased a beautiful little wooden clock from Alabama. Within a week, one of the clocks stopped working. I would have gladly paid a clock-maker to at least look at it, but due to scheduling that wasn't going to happen for a month, so I decided to open it up myself and just have a look.
And I'm very glad I did!
The spinning of the "balance wheels" on mine (and I suspect on most analog clocks) are stopped and released by thin little ribbons of metal attached to a kind of see-saw at the top of the mechanism. When a ribbon gently touches the wheel, it stops it from spinning. The other ribbon simultaneously rises to give clearance, so the other one can spin instead.
All I had to do was massage one of the ribbons back into place using a small screwdriver. Clearance of a mm less is all you need, it just has to be not touching. It's a bit tedious, but a super-easy fix, if that happens to be the problem.
IMO it's totally worth checking out, if one side of the clock is working and the other is not. Again, just resist the temptation to even TOUCH anything else!
I would say "good luck" if "luck" had anything to do with it!
Hello!
I was playing some blitz chess with my friend recently, but the game got so intense, that my chess clock fell down, and the minute hand fell out of place. Is it possible to somehow open it and put it back on? I unscrewed the screws, and took off plastic caps for hands, but the winders didn't seem to come off.
Grateful for any help, Ralfs