It looks like the screw that goes into the end of the pusher has snapped off. These are typically sold in generic lengths and cut to size and then slotted. There are a few thread sizes but it should be fairly standard for the diameter. I'd acid bath the pusher to extract the screw shaft if you cannot get it out by simpler means. The other half is probably floating around the inside of the watch. I'd get that out before it jams the movement and needs a full service. It will also act as a template to size the replacement properly, though it isn't too difficult to figure out. You may also be missing the spring, I can't tell for sure from the picture.