You don't have to actually render the midi tracks to audio tracks to accomplish this.
1. Insert your virtual instrument as done on the video and let Reaper create all the audio outputs.
2. Load your instruments in VE and in VE's mixer change each track's output to NET1/2, NET3/4, etc. This step will route the various VE channel's sounds to the audio outputs Reaper created for you in step 1.
3. Start creating midi tracks as posted earlier, OR I believe you can have Reaper do it for you by opening the FX panel for your VE track and in one of the menus you can have it create midi tracks for this effect.
4. So now you should have 1 track for VE, 16 tracks of midi all routed to VE and 32 tracks of audio. Again make sure you change the output of your VE channels to NET1/2, NET3/4, etc. or you won't hear sound coming out of each audio channel you've created. If you don't change the routing inside VE everything will sound out of the first audio track Reaper created in step 1.
Hope this makes sense. If I have time I'll put together some sort of tut on how to do this. I don't get the impression many here use Reaper, but I know there are a few of us out there :)