Hi,
From the Traffic Manager, its backend is Application Gateway. Application Gateway will have 2 set of backend pool, one for Images and another for Videos.
Traffic Manager can send probes to a http path to detect whether its backend is healthy or not. So, you can specify either image path or video path or a general path which defaults to a another page which responds with 200 OK.
App service monitoring will be done from Application Gateway. If Video App service is down, then Application Gateway will throw 502 to the client.
Do you have Application gateway and App Service in different region which needs to be load balanced via Traffic Manager ?
If that is the case, you might need to think about using Azure Front door where you can have path based rules on the Edges and you can add App Services directly as backend pool instead of Application gateway.
Regards,
Karthik Srinivas