Is there a zip with the included dependencies on the github? most extensions have releases with everything needed to run it in a .zip. in fact thats how the mediawiki releases work.
Topic on Extension talk:WikiMarkdown
I'm afraid that Composer is used so it can install dependencies in the vendor directory and update logs, which is not always something you can do by hand. An approach you could try is to run Composer on a local copy of your MediaWiki files inside something like Docker. Some people without access to a CLI have managed to run Composer from a PHP file, but I'm not sure how practical that would be.
I was able to fork the repo and make a github action that just runs composer and compiles up a .zip as a artifact.
I was able to just add "load_composer_autoloader": true, to the extension json and the .zip just worked no issue.
Somebody working on the repo with more time and experience with github actions than me could automate releases that do this for all supported php versions (which seems to just be 7.4 because all the other ones errored out) and then installation wouldn't require a cli at all!