If you know the exposure time the camera used in your photo Richard then you'll be able to get a rough estimate (for that specific case atleast)
Count the revolutions.
I assume this is the study you were thinking about.http://steinsharpe.com/nate/Strobe_Lab_files/Final%20Paper.pdf
They don't talk about the usual speed of a diabolo before tricks, but you'll be able to get a rough idea from their graphs (after 2 circular wrap accelerations etc). Most of it is in degrees per second, but just multiply that by 60s/360deg and you'll have RPM. They also mention the maximum speed achieved for each speed up method, so you'll be able to use that as well (It would be quite above the usual speed however).
The paper is form 2008 so diabolos may have changed a bit since then. However I think what decides the relative speeds of a diabolo would be axle diameter. Since the speed of a diabolo moving along the string during speed up would remain roughly constant, the axle diameter is what transfers this into angular velocity. Maybe check what the axle diameter of the diabolos they used and compare that to common ones these days.