Since the introduction of ICS (ice cream sandwich), Samsung has removed the UMS (USB Mass Storage) mode from all its devices. Axiomatically, it is not present in Galaxy S4 Zoom. But folks at galaxy phone have found a way on how to enable it.
Basically, what you need to do is get a pre rooted ROM for it and flash it. Then install the UMS utility for the Samsung Galaxy S4 in it and you are good to go.
You might be thinking why I just did not tell you to root it and install UMS application. The reason is that currently there is no way to root the Galaxy S4 Zoom and the only way to achieve root is by installing a ROM that is pre rooted.