Yes, this is the intended way.
Some H5P packages have content types that require and depend on certain library support files to be present to work. You will see that the error message says, "Missing required library H5P.Image 1.1" etc in your example. That message tells us that those library files don't yet exist on your Moodle site. The admin needs to install those.
A related issue is versions. In your screenshot you will see that the admin has installed Mark The Words, but the error message is telling you it needs Mark The Words version 1.9. So the version on the server is probably too old (but also could too new!). Again, this is an admin task and they can check the versions over in Site admin > H5P > Manage H5P content types. It shows them every content type and every library with the version of each.
Right now, there is no tool to manage library and version control in H5P. So admins will have to track this information down manually themselves, which is not easy to come by. There is always the possibility that a teacher will upload a package whose library files aren't in Moodle yet or whose versions are wrong. When that happens, these sorts of messages will appear. However, once the right versions of a library file are installed the first time, any new content type will find them and install correctly.
Some H5P packages have content types that require and depend on certain library support files to be present to work. You will see that the error message says, "Missing required library H5P.Image 1.1" etc in your example. That message tells us that those library files don't yet exist on your Moodle site. The admin needs to install those.
A related issue is versions. In your screenshot you will see that the admin has installed Mark The Words, but the error message is telling you it needs Mark The Words version 1.9. So the version on the server is probably too old (but also could too new!). Again, this is an admin task and they can check the versions over in Site admin > H5P > Manage H5P content types. It shows them every content type and every library with the version of each.
Right now, there is no tool to manage library and version control in H5P. So admins will have to track this information down manually themselves, which is not easy to come by. There is always the possibility that a teacher will upload a package whose library files aren't in Moodle yet or whose versions are wrong. When that happens, these sorts of messages will appear. However, once the right versions of a library file are installed the first time, any new content type will find them and install correctly.