You can. Months ago I messaged GOG that it's completely illogical to sell the classic version (with HD patch applied) and launch the Extreme edition which is a complete different game to my opinion and many others.
Apparently they still think it's an expansion and not a kind of sequel and launch the Extreme edition as default.
So I've taken my own action and manually changed which game should launch first. It's very easy (so thank you GOG for implementing it in this way, it helps a lot :) ).
Below are the steps to alter the required file manually. If you don't want to alter such files by yourself you can skip these steps as I've included my version of the file below (make sure you have a backup just in case).
This is what you need to do in 5 easy steps: 1) Locate the game installation folder.
If you don't know how to do this open GOG Galaxy and go to the game. Click on the "More ↓" menu and go to "Manage installation" and click on "Show folder".
2) Locate a file that has the name "goggame-1207658713", or at least goggame- with some numbers.
It's a ini file which you can open with notepad (I prefer notepad++, but if you don't know what it is just go with notepad).
3) Make a backup(!) of the file and place it somewhere outside the game installation directory.
Making a backup is as easy as making a copy of the file and placing it on your desktop for example.
4) Edit the file in notepad(++) and swap around the 'path' of "Stronghold_Crusader_Extreme.EXE" with "Stronghold Crusader.exe".
Also change the name "Stronghold Crusader" to "Stronghold Crusader Extreme HD" of the cluster you just changed to the extreme edition.
5) Save the file and restart GOG Galaxy. It should now start the original game (HD edition) with the big play button as it should have done by default.
If it doesn't work please let me know. It is possible that you need to re-add the game by using the import feature, but if I remember correctly it should just work fine with a restart (GOG Galaxy 1.1.25). ---
You could also make a backup of your goggame-1207658713(.ini) file, for example move it to a different directory, and place my version of it in the installation folder (see step 1 on how to locate the installation folder). I've attached a link to my corrected version at the bottom this post. Replacing the original file with my corrected version is easier than manually editing it but you can chose either way.
If you have more games you'd like to change this way I'd recommend to look around in the file structure. GOG really made a great effort in making the file format easy and understandable. :)
DOWNLOAD goggame-1207658713.info