While I generally agree with Matt... You can do this. I've used it extensively on my video wall to run videos and it works well.
1. Create a zone specifically for the remote display.
2. Then, in MC, switch to this new zone and play a video.
3. Right click on the video and choose "Detach Display". This will pop the video out into its own window.
4. Move this detached window over to the remote display (just drag it, or use an application like Ultramon to send it directly) and double click it to go fullscreen.
Okay, now, as long as you don't "resize" that detached display (don't ever make it not fullscreen again, just open and close it as needed), you can set up a command to automatically switch to the zone and detach the display, like this:
'Detach display on Zone 1
mc17.exe /MCC 10037, 1:0
MC remembers the position and size of detached displays on a per-zone basis. So, you can just use that zone (and re-detach the display) whenever you want to play to the remote display.
Here's an example script that I had set to run at startup on our Video Wall:
<package>
<job id="vbs">
<script language="VBScript">
'Create our handy dandy Shell object
set WshShell = WScript.CreateObject("WScript.Shell")
'SCRIPT ACTUALLY STARTS DOING STUFF HERE
'Pause for a bit
WScript.Sleep 60000
'Start MC
WshShell.Run "mc17.exe"
'Pause for a bit
WScript.Sleep 1000
'Detach display on Zone 1
WshShell.Run "mc17.exe /MCC 10037, 1:0"
'Pause for a bit
WScript.Sleep 1000
'Run wallvideo playlist
WshShell.Run "mc17.exe /Play TREEPATH=Playlists\WallVideo"
</script>
</job>
</package>