Yep, that's broken.
When last I mentioned it, my Sega CD Model 2 was as above - spindle-less. Here is the remainder of the story... unfortunately, it does not end happily.
The first repair attempt centered around this 1990's Sony Car Discman. As you can see, it used the same type of magnetic spindle as used in the Sega CD - in which the disc is held in place by magnets on either side. The spindles were exactly identical in size and shape, as well as magnetically compatible. This could have been an almost-OEM solution, except...
Upon disassembly, I found just one minor issue with this plan... the spindle was not designed to be removed from the motor. This idea had to be scrapped in favor of my next plan.
Playstation spindles: horribly fragile, but readily available and just the right size.
I ordered a Playstation replacement spindle - as it turns out, these are just the right size for the Sega CD's disc assembly. It pushes right down in place, and away you go.
So, I removed the magnetic pieces from the drive lid and snapped this spindle in place. It holds the disc securely above the casing, so no more scraping inside. Brilliant, except... well, now the motor won't spin up.
I blame my cat, who won't stop climbing all over it, opening the drive door and turning it on while I sleep. I'd guess somewhere in the time between repair attempts, it stopped spinning up.
Regardless - buying a replacement would officially push the amount spent on parts over the cost to buy a new unit. So, for now, we're done. Depressing, but we'll find another.