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A spindle moulder is basically a big router.
The main difference is with a router you buy a profile and attach it to the router by putting the shank of the bit into the routers collett. With a spindle moulder you buy components and build your desired profile buy placing them on the spindle of the machine.
With relatively simple profiles like skirting boards it is possible to use an autofeed a guitar neck is quite a complex profile as it changes along the length of the neck. In that video the operator is using a jig to guide his cut as well as using the jig to hold the workpiece. As you say there is no loose clothing to catch and drag him onto the cutting head and he's not wearing gloves so that particular issue has been thought about and addressed. In a modern setting there would likely be some sort of safety gear above where the jig is moving to shut the machine down if something hits it and in Europe the cutting head would have to be braked so that it stopped within 10 seconds of the off switch being hit.
Really? That's nuts if so. I've never used one; I actually think I'd find it a bit intimidating tbh. The few I've seen have gates and guards on them, where just enough of the cutter is left exposed to make the cut you want - not just a mental death blade in middle of a table.
At least he's not wearing a tie...