The small air compressor without a storage tank will not blow anything. The compressor prodces a small volume of air. Put that air into a closed outlet, a tire or tank pressure can build up. But with a blow nozzle on the outlet of the compressor no pressure will build up and the compressor produces only a small volume.
I manage trying to wash dirt off the side of a building with water on a hot day. Your small compressor would be like using a teaspoon. Canned air would be like using a large picture of water. And an air compressor with a tank would be like using a bucket with a hose replacing the water used. The size of the hose would compare to the compressor size.
They must have copied and pasted that warning from one of their air tools, without really thinking about it (I would guess they can’t read English). Yes, compressors compress air.
BTW, I have one of these (or a very similar one, from Checker Auto), and it works GREAT. I’ve used it for many years.
So this one will do the blow thing I want, seeing as how it has the tank?
I don’t know about overkill, more overprice. The one I’m looking at is $39 with the coupon, and that’s about the limit I’m willing to go, plus I want it to multi-task: inflate tires as well as blow.