Mopidy’s HTTP RPC requires HTTP POST requests, not GET. You can’t fire these off from bookmarks like you want.
Since you don’t seem to be entertaining the idea of helping to improve the PiMusicbox web client, why don’t you try one of the other web clients, perhaps one of those would be more to your taste? If you install the very latest v0.7.0RC4 at https://github.com/pimusicbox/pimusicbox/releases/tag/v0.7.0RC4 you can use moped, mopidy-mobile, mopify, simple-webclient or kuechenradio. If you are still using v0.6 then only some of those will work, I don’t remember which.