There are no catches here -- simply visit the official giveaway page and grab your copy, completely DRM-free. That means you can install the game on multiple systems and run it at will without any online checks or restrictions.
With that said, GOG's website appears to be suffering from a few server errors at the moment (possibly due to high demand, or the ongoing Summer Sale). As such, if you have issues claiming your copy of the game directly from the Absolution store page, try visiting the main GOG storefront and scrolling down a bit until you see the Absolution giveaway banner.
If you're logged in, there should be a claim button on the right. Just click that, and the game should appear in your library shortly after.
Absolution is a fantastic stealth game in its own right, but it was a major departure from previous games in the franchise. Instead of throwing players into an open-ended level with a handful of targets to assassinate (and complete freedom to do so however they wish), Absolution is much more story-focused, with linear levels and fewer equipment customization opportunities.
Nonetheless, the game's graphics and gameplay still hold up well today, and it currently has a 3.9/5 rating on GOG, which is far from terrible. If you need something to keep you occupied until Hitman 3 drops, you could certainly do much worse than Hitman: Absolution.