You've moved the beta exe out of its folder and replaced the normal exe with it, yes? That way Steam Overlay will work? Because if you were linking to the normal exe in that shortcut it wouldn't work correctly with the Steam version. Check the details of the exe your target line is pointing to and see if its version is 1.59.79384, and if it isn't then you've replaced your normal exe with the beta one.
If you have done that and haven't backed up your normal exe then just validate OA's cache using Steam and it should re-download the proper one. If you no longer have the beta exe in its folder, then you need to re-download the beta patch you were trying to use, delete your beta folder and reinstall it. Once that's done the best way to get it to work properly is to use the _runA2CO_beta.cmd file in your OA root directory. Personally, I have a bunch of my own bat files set up to run various mods of my choosing. Here's one, for example:
Edit: Never mind about the not being able to directly link to the exe thing I posted, just tested and it seems you can. Still, the only time this error has come up is when someone's using the beta patch incorrectly.
set _EXE=C:\Steam\steamapps\common\arma 2 operation arrowhead\Expansion\beta\arma2oa.exe
set _A2=C:\Steam\steamapps\common\arma 2
set _PROFILES=C:\Steam\steamapps\common\arma 2 operation arrowhead\Profiles
set _MODS=D:\ARMA 2\
call "%_EXE%" -noSplash -showScriptErrors "-profiles=%_PROFILES%" "-name=Zipper5" "-world=Desert_E" "-mod=%_A2%;Expansion;CA;Expansion\beta;Expansion\beta\expansion;%_MODS%@CBA;%_MODS%@ACEX_SM;%_MODS%@Blastcore_Visuals_R1.2;%_MODS%@PROPER;%_MODS%@TrueUser;%_MODS%@VFTCAS"