Funnily enough, I just dug this out yesterday to start trying some scenic painting and weathering using an airbrush. I got it about eight years ago and it has lain unused till now.
...which looks just like yours, but with a reservoir tank fitted. I did run it yesterday and today again when I took the picture and it seems to work very well. I've set the regulator to about 20psi and it seems to get up to that quite quickly and then maintain it with the pump stopping and starting when necessary. The only possible problem I noted yesterday was that the motor got quite hot when I first started running it. This could have been that the regulator was set to quite a high pressure and the pump was running continuously for several minutes until I got it adjusted down to 20psi. I've just run the unit for a period and simulated use at 20psi and the motor doesn't get more than just warm.
I'm not sure how it might run with no tank.
[Later] Just noticed I've not really shown the regulator and water trap being the same as you show...
...it's set on the end of the tank.
Jim.