Can I enter a giveaway, if I have an obsolete version of the game?

It mostly depends on the creator, but usually doesn't really liked - other people doesn't own the game at all, sorry :\

yeah that allowed in the rules. but just to be sure, ask the ga creator if it's ok since some people will take offense and probably blacklist you.

According to the SG rules, you may always enter if it's not the exact same game.

If it's essentially a bundle/package [ie, you've a base game and they're basically offering a version with DLC], then they may choose to take a reroll, as they always can with such circumstances.

If they're completely different editions, you can always enter, though as adam noted, people may not always appreciate what can sometimes come across as notable, selfish greed.

In the case of the augmented edition it is functionally the same as the base game (but with exclusive features), while Director's Cut is GOTY.
So they can choose to take a reroll if all the DLC of the [goty] package is still purchasable- which, in the case of Human Revolution, it no longer seems to be.

As such, since this is the *only way for you to get The Missing Link DLC, it likely won't qualify for a reroll.

*However, it seems to still be available through the Deus Ex complete pack. Which might qualify it for a reroll.

tl;dr, it's not entirely clear in this circumstance, but you should theoretically be able to enter Director's Cut giveaways.

If you explain the circumstances I noted above as you enter (or at least when you win), it's unlikely too many people would take umbrage at you entering.