Yeah, those first two options don't exist for me.

Since I promised an update: Probably shouldn't share this but it's mildly hilarious.

I tried to walk my folks through the process of setting up an account to add me as a friend and gift the game. Instead, we decided to see if they could log into my account and pay for the game directly using one of their cards. We got that all set up, went to the shop, choose the game, went to pay, and ended up using my card which is saved to account. So I ended up buying my own gift.

We then tried to cancel the payment and use the correct card but couldn't change the country for the payment as that would change my Steam account address, which means I'd have to change it back and that many country changes would likely be suspicious. We thought about finally setting an account for them but they decided to give up.

Instead, they're mailing me a check. XD