How to make Instant Hot Chocolate Taste Less Watery
I can think of four possible fixes.  One is simply, use less water - a smaller amount of a richer drink may well be preferable to a larger amount of a watery drink.  Another is the reverse, use more mix, which uses two packets (if not all of the second is necessary, you might share with someone else who wants extra, save it for next time, or simply discard).

Third option would be to add a pinch of salt.  It can help balance the flavors (a pinch isn't enough to make it not-sweet), and it's commonly described that less salt can make something taste "watery", and adding a touch of salt makes things taste more balanced.  It will change the flavor a bit, but not necessarily badly.

Fourth option is to add stuff.  Sugar, creamer powder, spices (possibly brought from home), whatever pleases you - and some of which might already be present for doctoring coffee.  Any of these options should add some flavor, changing the taste but perhaps not badly.  I wouldn't recommend milk, since (as you mention) it has enough liquid it can dilute the flavors, but powdered flavorings might help (and not dilute).  Or you might even try keeping on hand a candy to dissolve in your drink (peppermint round, wrapped caramel) the heat and water should let it dissolve a burst of flavor into your drink.  Again, flavored, but not necessarily bad.