How do I determine the "length" of this derailleur?
It looks a lot like the Shimano TY-300-SGS on the product page, which would be a long cage rear derailleur.
However there's no strict guarantee that the current derailleur is the best one for the job, and the definition of short, medium, long changes with time. There are other specs on the product page, like total capacity, low sprocket min/max, etc, which you can check are suitable for your gearing. Sometimes it's better to check the specs first rather than just choose medium or long.
You might find that you could select a shorter length cage for your needs, which could give better ground clearance with those small wheels, for example.