I have a Troy-Bilt mower, the next size up, and the same thing happened to me last year. I think that you will find that the part that plastic thing presses into is still in the block and IT does have threads. I ordered another plastic drain plug off of Ebay, but before it arrived I discovered that a 3/8 hex head brass pipe plug will screw right in and work even better for me.
Good Luck,
Roy