Insufficient views to determine what needs to be done. Does the end of the handle slip onto the shaft under the table? If yes, we need to see what the shape of the hole on the handle is, end on.
Those small machine screw holes in the side of the handle... are those threaded?
I'm going to guess that the two screw holes are threaded. The handle slips onto the shaft so that the screw holes are on the flat side of the shaft. Then, you need two small machine screws to thread into the handle to act as set screws.
If the holes are not threaded, then perhaps the machine screws slip through the handle and are threaded into threaded holes on the shaft.
Either way, should be an easy fix, needing only to find the correct machine screws, something like this, I'd expect.
