Yeah, the mount is part of the deluxe edition
To explain how it works:
Once you own the mount, you will receive it in game probably in the mail, as that’s how they used to give out stuff like this, on all of your characters, including new ones made after purchase (I assume, I haven’t heard confirmation but they’ve never given mounts for only one character as far as I’m aware, especially not for deluxe editions). The mount scales to your riding level, though I assume it cannot fly as I don’t see how a warpstalker would fly, but I have not seen confirmation on that either
The key is you only have the mount, not the training. You will still have to purchase that yourself, which in TBC is the bulk of the cost for riding, your 60% and 100% mounts together only come out to about 100g total before rep bonuses, so people crying about how the mount is pay to win I guess regularly just throw their gold away or something because 100g in TBC is barely more than pocket change…