Does anybody know why antiX doesn't understand the idea of trying to run a script or a portable software application?

Here's what happens. I check carefully that the file in question is executable. I double-click to run it. A box appears, asking me what application I want to run it in.

The operating system doesn't seem to understand that (for example) a script or an appimage is supposed to run 'in its own right', not in some other software that the user needs to specify.

I've never seen this error in Puppy, Slax or Porteus, or even in Ubuntu or Mint, so why does it happen in antiX (and some other systems, eg. Shibainu, Vector and Slitaz)?

More important, how can I get antiX to run executables at my request in the normal way?

First of all, antiX uses single click not double click.
What file manager are you clicking from?
Which version of antiX are you using?