I would hope that you would have found the bit we thought was missing off the end of the stem. In general a stem looks something like this:
If you compare that to yours it seemed to us that a bit is missing off the end. It would be good to find that bit. If it is kicking round inside the movement it could be a problem. If it is still located then it will prevent you pushing the new stem in - my first impression is that it is not still located but heaven knows where it has gone if it has indeed gone. If you have had a look at Marks vids about stem removal then it will direct you to the place on your watch that says "push" and has a little arrow indicating what to push, this may need to be pushed gently to release any bit still lodged in or to push a new stem in, but to be more sure we would need a close up pic of the stem and crown out of the watch.
The square bit on the end of the stem fits through some crowns or cogs that turn the pointers. The place on the stem in between the square bit and the screw thread is where the stem is held in and you gently push down where indicated to release the stem which normally comes out whole, in your case your stem is already loose lending creedence to the idea that the missing bit is still in there (unless it has dropped out already) if it has dropped out of the watch the next step would be a new stem. It may be that a new stem might fit in with no further work - if you are lucky.
I regret that there are a few scenarios here but we will take them one at a time.
If you find a new stem will not go in then you may have to remove the plate on the top hopefully it lifts straight off when the screws are undone but never having worked on one I honestly don't know. With that plate off you may get a clear view of the place the stem should go into.
If you do have to remove the movement don't forget about the push buttons that will need to be eased back and of course the stem should be out, It may be possible to turn the watch movement around once it is out to see if anything drops out.
Cheers,
Vic