That repro is made as a non-firing gun; the maker says it is sold as a firearm and can be made to fire, but does not recommend doing that. So, it is effectively a dummy.
Making a single shot "zip gun" is easy. But making a repro Liberator in the way the originals were made would require a lot of very expensive machinery, including stamping presses and spot welders, machines usually found in (surprise!) automobile factories.
I have a Liberator, and have fired it two shots just to see if it worked. It did, but I am not going to toss my Model 19 or M1911A1 and use the Liberator.
There is a lot of misinformation about those guns, mostly by people selling one. They were never dropped anywhere in Europe to anyone at any time. The ones sent over kicked around depots with no one wanting them and were finally dumped in the ocean after the war. A few were reportedly used in the Pacific, but the only documented use was by Philippine police right after the war until they could get something better. A few turned up in China.
There seems to be no solid evidence that any Liberator pistols were ever used against the enemy, ever killed an enemy soldier, or ever "liberated" anyone. It probably seemed like a good idea when someone said it fast, but in the end it was just another waste of money.
BTW, in spite of the smooth bore, BATFE has specifically removed them from the purview of the NFA and designated them curios and relics. There is no need under federal law to put a number or any other marking on the originals.