Gift Link Through E-mail

At Steam? Only with inventory gifts (old or by multiple pack etc).

Yes. better be more precise in your question

FAQ https://www.steamgifts.com/about/faq

How do the "Gift" and "Key" options work when creating a giveaway, and sending my gift?
When creating a giveaway you have the option to choose either "Gift" or "Key". The two are interchangeable, and after your giveaway ends, you can add or remove keys regardless of the option you select when creating your giveaway.
Gift
You'll want to choose this option when you plan to send a Steam gift to your winner, or if you would like to add keys to your giveaway after it ends. Once your giveaway is complete, you'll be able to see the winner, along with their email address. You can then choose to either send the winner an email, or a message on Steam to deliver your gift. Once the gift is sent you'll want to check the "Sent Gift" checkbox next to the winner as a reminder that you're finished with the giveaway. If you prefer to send a Steam key through our site, you can click the "Add Key" button that's displayed beside the winner. You can then enter a key and click "Save" to assign the key to the winner. At that point, the key will not yet be visible to the winner. They will only be able to see the key on our site when you check the "Send Key" checkbox. If you uncheck that box at any time, they will no longer be able to see the key. An icon with an eye will appear next to the key once it has been viewed by the winner.
Key
If you choose this option, you will be required to enter one or more Steam keys when creating your giveaway. Once your giveaway is complete, you'll be able to see your winner, along with their email address. You'll notice the key you previously entered is displayed next to their username, along with buttons to modify or delete the key if necessary. At that point, the key will not yet be visible to the winner. They will only be able to see the key on our site when you check the "Send Key" checkbox. If you uncheck that box at any time, they will no longer be able to see the key. An icon with an eye will appear next to the key once it has been viewed by the winner.
If you create a giveaway for 50 keys or greater, the "Send Key" checkbox for each winner will be automatically selected. This means the keys will be instantly available to your winners the moment your giveaway ends. This is done to make the experience more convenient when managing giveaways with a higher number of keys.

Is it possible to send a Steam, or Humble Bundle gift link to my winner through the site?
Yes, you can follow the instructions for using a Steam key as described above, but enter a gift link rather than a Steam key. The gift link must be entered in one of the below formats.
https://store.steampowered.com/account/ackgift/XXX
https://www.humblebundle.com/gift?key=XXX
https://www.humblebundle.com/?gift=XXX

I think that the gift link was working properly about two weeks ago. now? I do not know.

only with gifts in your inventory - since 2-3 years ago, the games you buy on the store can be directly gifted to friends so you have to add the winner of your giveaways and send directly to them if this is the case, if you have instead an inventory gift unopened that can be sent by mail