It probably means a crime where there is also a drug related indictment (or conviction, not sure which). Your example would be a crime of robbery, plus possession.

I wonder how many cases of 'drug related crime' are just defendants who were arrested for another crime while they had small time possession?

Both. The numbers are skewed.

If you're sitting on your driveway in a chair with a beer and your neighbor backs his car into you, it's an alcohol related accident.