There are devices you can buy that will drain the battery and measure their total mah. The IMAX B6 or something I remember will do the job perfectly for you.
As far as that thing you bought the panel is only 1.5w and the battery or device output is 5v at 2.1A so 10.5w output.
It clearly as you said is not 100ah. If it was it would be a 500 watt hour battery and lol, clearly impossible.
Chinese, Maybe they put the numbers in wrong or even deliberately tricking people.
I would say it's probably like 1ah which would be 5 watt hours.
So it could output 5 watts for an hour or the 10.5w output it does for nearly half an hour. Then the little panel will take say roughly 4 hours in the sun to charge the battery back up. That is about...