I don't own all the champions, but I got a Mystery Skin instead

There's your issue, you have <10.

You need to have at least 10 champions above a 520 RP cost. Not sure if it's affected by sales but it seems it was for me :/

On a side note; pressing Windows Key + Alt + Prnt Scrn for a screenshot will copy only the active window rather than the whole screen, if you want to leave everything else out without cropping the image afterwards.

Only champions worth 520 RP or more are eligible to be received as a Mystery Champion. Anything less and they don't count towards the 10+ champion requirement.

Graves is on sale for 440 RP so doesn't count right now, unfortunately.

This is actually kind of a bullshit loophole imo, so if you wanted a champion instead of a mystery skin I'd suggest you submit a Support Ticket and let them know you only fell below the limit due to the sale and would very much be pleased if they were so kind as to take their precious time to help you.

At least 10, not at least 11.

WHAT ARE THE REQUIREMENTS FOR GIFTING TO FRIENDS? The player receiving the gift needs to have been on your buddy list for at least one day. The player receiving the gift cannot be banned or suspended (this includes LeaverBuster, Tribunal, etc). The player sending the gift must be at least level 10.

For Mystery Skins: The player receiving the gift must have at least 10 unowned skins that they are eligible to receive for champions they own. For Mystery Champions: The player receiving the gift must have at least 10 unowned champions.

https://support.riotgames.com/hc/en-us/articles/201752934-Mystery-Gifting-FAQ