I've had some success launching apps through wine from the Linux Steam client. As Michael suggests, you need to use a shell script to launch them.
For example, I use this to launch path of exile, named
cd "Path of Exile"
The game wouldn't launch for me without unsetting LD_PRELOAD. Also, the permissions on the file had to be executable.
I set the permissions on the script (for example):
chmod 755 ~/bin/poe.exe
Then I use the Add non-steam game option, and then I browse to the script.
So, that's how you add a generic wine game...
To answer your question and to add a steam game, you need to create a script that calls the steam.exe and passes the game id. This will result in launching a second instance of steam, but you wont have needed to have it running for the whole time, just while the second game is running. So here's another script that kicks off the windows version of unturned by calling the windows steam client through wine with an appropriate url:
cd Program\ Files\ \(x86\)/Steam/
nice -n 19 wine Steam.exe -no-dwrite steam://rungameid/304930
In this case I don't know that the unset on LD_PRELOAD is needed, but my other scripts used it.
NOTE: The WINEPREFIX only needs to be specified if you specified a WINEPREFIX when installing steam (or other windows programs). If you didn't specify one when installing steam for windows, then you wouldn't need one in your scripts. And if that's the case, you will want to replace it with