The Dremel is a fairly straight forward direct drive drill. There's not a lot to go wrong. There are the brushes and the bearings (sleeve on mine) that are repairable. Then there is the armature itself. If the armature has a short or open, the simplest solution is just to replace the tool. Dremel has "upgraded" their models, and diversified, to the point that fitting up parts to old tools is a hit or miss proposition.
My Dremel(s) have been around a long time. One of them 30 plus years. Hell, I've been married this time for 30 years. Call it 40-50 years old. But they don't get used often. The oldest one has had a new set of brushes about 20 years ago. The newest one has a "turn button" for speed control. I've never had an armature fail, but it could easily happen. Listening to your video, it sounds like a dry bearing. Or possibly an armature segment shorted. I do have a "growler", the test fixture for armatures. But I haven't used it in so long, I probably couldn't distinguish an error any more. Repairing a small armature was a pain in the wazoo when I was in good shape. That was then. . .
I would say check the bearings and brushes. If they're OK, then just get a new one. The tool itself is still reasonable if bought alone. The "kits" is where the price goes up, fast. For what it's worth, the one you display is a fairly new model. Parts should still be available. One of mine is so old there are no parts available. Even the aftermarket bushings for solid mounting don't go back that far.
In passing, I had a "drill press" adapter for one of the old ones. Even the older model was too unstable for doing circuit board work. The net result was a Horrible Fright bench top mill as a drill press.
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