Well, when you have the Soundblaster connected, what other options exist under "More" menu, if any?
The Quickstart Guide for the Soundblaster says that it is operational without drivers. The drivers just add more features. So that means that Windows would see the output as digital, I think, although the manual is silent on anything to do with the Windows Audio Devices used.
Basically, Direct Sound works because Windows knows what it is, and will convert the audio format to match the Soundblaster capabilities.
You need to select the correct Soundblaster Digital output on your tablet, using WASAPI in Exclusive mode hopefully, and make sure that the Soundblaster is capable of playing/decoding the audio format that you send to it. Using WASAPI Exclusive mode means Windows will not be able to convert the format, which is good because you get better sound quality, but bad if the Soundblaster isn't capable of playing the format.
So inside JRiver MC, select the correct Soundblaster Digital Output, and it should work. Leave the Windows default audio device set to the local speakers in the tablet, so that audio can play through those when you aren't using MC.