I don't know why Discord refuses to recognize the old EQ clients. I had the same problem, and wanted to have Discord recognize I was playing P99 so friends would know that I might be in a group or something as a reason I may not be responsive to their messages.
I finally decided to just make my own tiny app that opens a minimized dummy window (so Discord can recognize it), launches EQ, then quits itself once quit out of EQ. Works for both Project 1999 and Project Quarm. You just have to put the app in the same main folder as P99/PQ (alongside eqgame.exe, since it will only look for it in the same folder it's in), and then make your shortcut point to this app instead.
It's a pretty simple app, and in case anyone else like yourself wants it I put it up on my web site. If you don't trust me, the .zip includes the full source code so you can build it yourself instead of using the pre-compiled .exe included inside. Here's the link:
http://zauron.net/downloads/EQForDiscord.zip
NOTE: This will only help with the "Now playing" message appearing as your Discord status, set up by adding the app to Discord's "Registered Games" section of Settings and renaming it to EverQuest or whatever in those settings once added. It will not help if you want to use the Discord overlay with P99.