You can't give gifts on YT any more than you can give gifts on shabbat. But if you can use it on YT, or it add to YT joy it's ok. So what's up with permitting a gift of tefillin which, although you can't use it on YT, is a joyful gift. What's up with that? What gift would you NOT be able to receive?

Can you send gifts on YT that you'd have to do something (that's assur on YT) in the week to be able to use it?

I just got through learning this in the gemorah, and have a tough time wrapping my head around this one.

The ArtScroll Halachos of Yom Tov book isn't very helpful - it just references the psak in the Shulchan Aruch.You mean the person gets the gift on YT, but can't use it till after YT b/c it would involve a desecration of YT? No. Is that what you mean?

Both Rashi and Tosafos on the Gemorah in Beitzah 15a [d"h Hachi K'amar] writes that putting on teffilin on YT is not assur (unlike spiked shoes).So sending it on Yom tov would be Ok.
I always thought teffilin were muktzeh,thus assur! Am I mistaken?

is that not circular?

Isn't it the other way around?
Also, aren't they ksl, so if you'd need it, you'd be able to use it?