Why can't I use the delete-empty-src-dirs flag on Linux?

On Windows, I can run a command to move a file from my desktop to my remote like this:

rclone move src remote:dest --delete-empty-src-dirs --progress

but on Linux, this command complains about the flags. Are there different usages for some things on Linux than on Windows? What things are different?

Probably because you have an old version.

rclone version shows what?

Ah, it's 1.36. I'll have to update that. Sorry about that

Be advised that lots of Linux repositories have really old and outdated versions.
1.36 is downright ancient...
It is highly adviced you install directly from rclone.org - you can get traditional packages, but there is even a one-liner script you can copypaste to terminal to install in seconds.

not much is different.

for example, the same config file, can be shared between windows and linux.

Yea, there is basically no difference except that on windows you are probably going to use back-slashes in paths rather than forward slashes (except in the config file). On windows you also use WinFSP instead of FUSE to support mounts. Aside from that you can pretty much move any rclone setup around to whatever supported platform you want.