In this case, it may be more accurate to call it a Rereleased version, rather than a Remastered version, as it's closer to a GOTY touch-up than an actual Remaster (given the lack of attention to graphical or similar elements, and in how its content is arranged):

Due to a publisher change surrounding Kingdoms of Amalur, this version is no longer available [and has been re-released as Kingdoms of Amalur: Re-Reckoning]." " Re-Reckoning adds a new difficulty setting and updates the back-end rules for spawning loot, but it brings little in the way of graphical upgrades.""This version of the game will include [all DLC content] in one nice little package"

Moving past that passing bit of information, your point is a noteworthy one, as SG treats this as an entirely different game (due to the completely different APPIDs) from the rereleased version. Change Giveaway Game tickets are typically rather uncertain to qualify for, so it's always best to double-check these things.

Do please note that I'm not adding the info on the Re-Reckoning release to nitpick your phrasing*, but because I thought it'd be potentially useful clarify the differences between the Reckoning and Re-Reckoning versions to anyone coming across these posts who is unfamiliar with the differences between the two versions.

* ( Which by no means is inherently inaccurate, given how arbitrarily edition labels can sometimes be assigned. Specifically, this'd be in line with a "Definitive Edition" x GOTY (eg,Van Helsing: Final Cut), not to be confused with "Definitive Edition" x Enhanced Edition (eg, Age of Empires: Definitive Edition**)... and that's honestly too convolutedly specific for me to expect consistency in conversation on. :P )

** ( Though as shoddily done as those are, it's hard to consider them "Enhanced".. -,-; )

Could be an older key, ofcourse. It seems i still have the old version on my wishlist. Oddly enough it says: Release date: Expected soon.