Run two separate checks
Use a supported current player and confirm the developer before opening your account or playlist. Play one item, then test the same item with the intended external output. Record whether the player still shows the item, whether the receiver shows picture and where audio is routed.
Interpret the difference
If the Mac alone plays smoothly but the television output fails, compare the output route and audio settings with a known-compatible item. If the player cannot load the same source locally, review the account and stream format first.