This one day offer can't be used to renew a Prime membership, but can be sent to, say, a spouse. It seems that it can also be sent at a later date (perhaps when your own runs out) although we didn't attempt that.
If I wanted to renew my own Prime, I couldn't use a gift card balance, I had to use a credit card. Oddly, since I was giving a gift, I could use the gift card balance (still from last year's tax refund!)
I'm tempted to send a second gift to start next year (yes, it's possible). We split with family, so it's pretty cheap overall.