You won't get the textual info (TGIDs) showing up in a plain old audio player, no, but VLC or even MPC-HC can play the wav file you created and they should automagically load the .srt file (it's a standard subtitle format text file, however there are many different types of subtitle files, that one is the most common) and hence when you play the audio file in a proper media player (not just something for audio) you will get a display of the textual info from the .srt file.
DSD+ doesn't offer the option itself to show talkgroup info for DMR/MOTOTRBO or NXDN systems, perhaps in the future it might happen if the author of the program has intentions to release updates (at least that's what all of us hope he/she will do, pretty please) and take our requests for additional features such as displaying more information for these other systems.
P25 is so well established and known over the past 15 years or so that it's somewhat easy for devs to work with in terms of decoding things, but DMR/MOTOTBRO and NXDN and some other newer digital protocols are still not nearly as popular or well supported.
You can do what you're hoping to do, you just can't do it with DSD+ as the playback device, you have to use the default recordings that DSD+ makes and then play them back with either VLC or MPC-HC (I prefer MPC-HC myself but YMMV).