So I thought you could do it by going to your flows for that device and you have the option to route but as I just checked on mine it doesn’t give me the option to route a particular flow thru a VPN so I’m assuming you can’t.
Here’s what I previously used for sports streaming on the Apple TV. (AFAIK, this doesn’t work for all streaming services. I couldn’t get Netflix to show me international content.)
Using the network flows, I identified the servers used by MLB/Sportsnet/etc. and added them to a target list.
For what it’s worth, YES network just launched their direct to consumer in-network streaming service today for Yankees games. Probably more expensive then the MLB.TV/VPN route, but just wanted to mention it in case you were not aware.
I did that recently, just select the particular flow, choose Route at the bottom and select the device and VPN interface. You can also create a target list with on the web page with multiple domains and setup a Route to use that target list and select the VPN interface.