Is this game complete?
Nope. The actual game is in pre-order. You can pay for beta if you want access early, and you get to play the incomplete game as they build it, and give feedback and suggestions, which they can use to improve the game as they go. Can be a pretty nice idea, when communication is good between game developers and players. Currently only one romance route is fully complete (Moocha's), and they're starting on Finn's.
Basically, if you're someone who wants to play every route (rather than just a select few), and enjoys the idea of being able give feedback and suggestions, and would like having access to the beta, I would recommend giving it a go.
On the other hand, if you're someone who gets easily impatient, dislike the idea of having to communicate with the developers, or if you are someone who would get really annoyed by bugs or other problems, I'd recommend either buying the pre-order, or just waiting for the release.