How do I remove a Playlist in Apple Music on Mac when the 'Delete Playlist' option is missing?

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Just know that a Playlist is only links to the actual songs and no changes in the Playlist, including deleting or duplicating, has any effect on the original song. They are not folders that actually store the songs. It is not as clear on the Mac that your Playlists are stored in the Library, where on the iPhone, the Library tab includes your Playlists and semantically it may make more sense for it to say Delete from Library on the iPhone. I do understand where it could cause confusion, or at least in the delete message they could make it clear that the songs will not be deleted from your Library.

This instructions you included are CORRECT and state that "If you delete a playlist, the songs in the playlist remain in your library and on your computer" and to delete a playlist it says "Control-click a playlist in the sidebar, then choose Delete from Library".

When you choose the option to Delete the Playlist from your Library, it should only be the Playlist that is removed from your Library. I just verified this myself and when I choose Delete from Library on a Playlist, all the Songs that were in the Playlist are still available when looking in my Library.

Choose Delete from Library on that Playlist, then choose Songs above in the sidebar under the Library section and those Songs should still be there for you to add to a different Playlist if you wish.