Adapted from https://www.youtube.com/watch?v=pykMfsdPLNY&lc=z13vfvtiflzqfluqo04chvd5irbpthtphqo0k.1462381366893673

The key to this technique is that you trick Steam into recognising Battle.net.exe as "Overwatch".

Create a non-Steam game with the following shortcut:

Target:
"C:\Program Files (x86)\Battle.net\Battle.net.exe" battlenet://Pro
Start In:
"C:\Program Files (x86)\Battle.net\"

battle.net://Pro is the internal Battle.net call for Overwatch.

Now *before* you launch Overwatch via Steam, make sure any existing instances of Battle.net are shut down (right click Battle.net system tray icon -> Exit).

You're ready to go now but something to be aware of...

By default the above will mean that each time you finish playing Overwatch you need to also shut down Battle.net, otherwise Steam will still think you are in game, since it thinks Battle.net.exe is the Overwatch process.

If this is too annoying, there is another option:

Go to Battle.net General Settings and Set "When I launch a game" to "Exit Battle.net Completely" and, optionally, check "Show a brief countdown instead of closing immediately".

This will cause Battle.net to automatically shut down when you launch Overwatch, however the trade-off is that Battle.net is also no longer running whilst you play Overwatch so you can't easily add friends/chat to them via Battle.net.