I believe that already exist and is called "AppImage".
Installing Docker or another container runtime is easy. I'd suggest creating a portable OS that you can boot from USB, or creating a local registry. You may also want to consider just creating a script to bind mount the binaries.
There are a number of ways to get this kind of functionality. Can you expound on "different computer"?
What part of "different computer" is confusing to you?
How different, for one.
Are they running the same OS? The same architecture? Do they have any software installed?