We upgraded to the $79 plan specifically to keep gift cards customers on our site instead of the alternative third-party GC app's that direct customers to there domain. We found out the hard way how valuable the recipient address is this holiday season. It costed us refunds and lots of confusion for customers. We'll be downgrading plans until this simple feature is developed.
On a side note, Shopify's price per share just reached an all time high of $1,285.19, way to go, I guess
This is a legitimate complaint and it's very unprofessional of Shopify to have not addressed this.
There are two workarounds I can think of which don't involve a paid (or any) app.
1) Instead of having the customer purchase a digital gift card, make a product listing for a gift card with the same denominations you would want for digital gift cards (this is what you would do if you were selling physical gift cards, and if you are, you can direct your customers to the same listing).
Rather than fulfilling the order by shipping physical cards, you can fulfill the order by issuing a gift card (from the Shopify app, under products-gift cards-issue gift card) to the intended recipient.
You can also issue the gift card to yourself (which would allow you to have access to the code) and then forward that email to your customer's intended gifted.
2) Have the purchaser temporarily change their email address to that of the intended recipient.
These are not optimal, but should work. Shopify has really dropped the ball by not fixing this glitch which has been brought to their attention numerous times.