What you did, opening the .wl file in the front end and hitting "Run Package", is not the correct way to load an external package. On top of that, the file you opened is the paclet info file, which doesn't really have any executable code so 'running' it doesn't do anything (and therefore doesn't give you any helpful error messages that you've done something wrong).
The instructions on the github page give a few methods for installing the package, did you try them and have issues? I think you can just run
PacletInstall["BioFormatsLink"]
and it should install.
