Your card has DSP v 4.12 — it's silk-screened on the chip in the bottom right corner of the empty socket. At least it is in this photo.
As far as I understand, right now you only have an SB16. That means that games you've played used SB16's PCM capabilities for digital sound and SB16's OPL3 chip/FM synthesizer for music. Not MIDI. This is why you don't have issues right now.
There are basically five main ways to connect MIDI stuff:
1) daughterboards to your SB16's Waveblaster header. This is what it looks like. These are cards like Dreamblaster X2, Roland SCB-55 and many more.
2) external GM modules like Roland SC-55/MT-32 or Yamaha MU-80 to your SB16's Gameport. This is what it looks like.
3) through a dedicated MPU controller like this.
4) you can also use dedicated ISA MIDI cards like Roland SCC-1/LAPC-I, Yamaha SW60XG and Turtle Beach Maui. They get MIDI instructions by themselves (and not through SB16) and simply feed audio output to your SB16 line-in port using a common audio jack cable.
5) finally, you can use two sound cards. Your SB16 will be used for digital sounds and OPL3 music (when needed), your second card can be almost any SB16 clone not made by Creative or ESS. The clone card is used only to control MIDI stuff using approaches 1 and 2. This is a more tricky approach as more hardware in DOS systems usually mean more conflict resources.
With your current card you should get hanging note bugs in scenarios 1 and 2, but not 3, 4 or 5. That means, when you play Doom with MIDI music, at some point you will hear a single stuck high note playing the whole time in the background of the soundtrack and it will be pretty noticeable.
P.S.: there are also cards with integrated MIDI capablities — SoundBlaster 16 AWE32/AWE64, Gravis Ultrasound and many more.
P.P.S.: you can find almost a lot of samples on YouTube and SoundCloud where people have recorded game music playing on any particular device. Doom's E1M1 is a track that you can find playing on almost any device imagineable.