Hi Frank,
I've never measured the compression pressure of a motorbike, but if I did I'd expect it to vary with throttle opening, regardless of whether it had atmospheric inlet valve or not. If the throttle is closed (tight), no/little air will enter the cylinder as the piston falls, there will be no/little air to compress as the piston rises, so the pressure in the cylinder will be relatively small at TDC. With the throttle fully open, there should be good filling of the cylinder, and thus good pressure when compressed.
So let's take 90 psi as the pressure with the engine spinning. To guess the compression ratio, we need to know a couple of things, particularly: when does the inlet valve close? With atmospheric inlet, probably just a little bit after BDC. (If the motor were from a DT or 90-Plus the inlet wouldn't close until well after BDC, so the pressure would be less for the same "theoretical" compression ratio.)
We also need some physics (sorry). If we assume the air in the cylinder is compressed adiabatically (no heat enters or leaves the system during the compression stroke - assumed in an Otto Cycle), 90 psi corresponds to a compression ratio of about 4:1, which seems entirely appropriate for a 1910 Douglas. (I know it's tempting to think that 90 psi means a compression ratio of 6:1 or more, but that's not how it works.)
In practical terms, if you pull the back wheel around you should feel quite strong resistance as each cylinder comes up on compression, but if the belt doesn't slip it should be (just) possible to pull the motor over each compression.
You're a lucky man to own such a fine little motorcycle: hope the riding season goes well for you.
Cheers
Leon