But I doubt you can gift someone a club which is above their level.
You are right, it is only allowed to gift up to the level of the recipient.
Some confusion is given to this by WGT, the link you posted states:
" What items can I send as gifts?
You can gift items from the Pro Shop that are available to all levels of players."
Which is at best misleading, but probably more accurately just plain wrong.
It's easily sorted though. If you want to send someone a gift above their level, try, when it doesn't work you'll be sure.
If someone is at level 50, can they gift someone else (level 90) a level 80 club? This is allowed.