This is not a question of installing the app. The .dmg file won't open - period. I can't install the app if the file doesn't open first. I've tried Stuffit Expander, right-click and chose Open, select file and use keys Command O, nothing happens.
I've not seen this before. Try opening a terminal window and "cd" to the location of the dmg file (for example, I'm assuming it is in your Downloads folder):
$ cd ~/Downloads $ open xdk_web_mac_master_3759.dmg
And, if that doesn't work, try this:
$ cd ~/Downloads $ sudo open xdk_web_mac_master_3759.dmg
In the second case you'll be asked for your system's "root" password (or administrator password). But the XDK might get installed in a location that you cannot start it from. Let me know if either of these work.