It works like that for all DLC, Steamgifts can't check DLC ownership.

Steam doesn't send out ownership data of DLCs (including any package that includes at least one DLC) through the public API, which is the one websites like SG use. Comparatively, SGTools also uses the private/personal API, which is why you have to be signed in to Steam Community for it, and why it can access information on things like DLC ownership.

There's various technical issues (including Steam Community login being infamously prone to quickly signing many of us out of it) that make it unsupportable for use on SG itself, though many userscripts also base in that second api, which is why they (specifically, SG++ and ESGST) can show things like which DLCs you own, warning you before you enter on giveaways for them.

In short, you'll always need to check ownership (by adding the user on Steam, loading the store page for the DLC, pulling up the "Friends who own this game" tab, and CTRL+Fing the username in question) for any giveaway you put out that includes at least one DLC. Or, for a likely less stressful approach, you could put up an SGTools filter for the giveaways that checks against the DLC ownership prior to entry, removing that hassle for you entirely.

In any case, thanks a bunch for putting this DLC up (especially given the technical complications of DLC giveaways, as noted)- it's frustrating getting these games where it's cheaper to buy a complete edition than the DLCs on their own, and where the game and sometimes even the complete edition have been bundled repeatedly, but the individual DLCs are a huge pain to get (hurting those of us who bought the base game). So this DLC- wihch is getting incredibly rare for giveaway- is much appreciated to be given a chance for. :)

Sorry if that's a bit of an overly long reply, I'm not good at being concise. :S