How did you configure Cubase in the first place? I've just tried and Dosbox midi playback through Halion Sonic SE with loopmidi port as an input worked (no stuck notes - I used DOOM as a test game) but I had to choose one track in Cubase and set its output midi channel to "any" as opposed to having 16 tracks with their separate midi channels. I then recorded the input of the loopmidi port on that track but got messy results on playback - timing is all over the place.

Are you trying to achieve anything else than real-time midi playback through Cubase though? To me it seems unnecessary complicated. A simpler option would be to use a standalone VST host (I use the free version of Cantabile). Load your Halion Sonic VST and set it to GM mode (Somehow I had to use the VST 2 version of the Halion plugin because the VST 3 one wouldn't respond to program change messages). Then configure loopmidi as an input in Cantabile and it should work perfectly. I haven't tried this, but I figure you could create a midi filter in cantabile that sends incoming channels to different VST plugins (as opposed to only using Halion), so you could create your own arrangements on the fly.

Thanks for the answer, I will try with different host. I'm just trying to achive best quality of realtime music playback, although I know it's not that simple because different plugins require different programming and it's not as simple as playing back the notes. Halion manages GM playback pretty good, but I guess using something like Hollywood Orchestra would give terrible results at the beginning (CC midi controllers are totally non standard).

I attach the screenshot of the settings. First just right click- add MIDI track (repeat 10 or 16 times), set channel numbers 1 to 16, attach them to the same instance of Halion and configure everything else like in the screenshot.