Hi,
The reason for the beta test is to get testing and bug reports/feedback. The reason for it being private is it's not ready for being public. You know, still alpha, feature-incomplete, in-progress. It doesn't help anybody to have mountains of forums discussing how much features X and Y suck when we know X and Y are only half done. It's actually a big distraction from development. Better to get a bit further first. This is also Donald's view, and most likely, you probably first read the Adventures cards when he previewed them after the game was manufactured.
That said... we are trying out this crazy idea of getting testers involved in the process as soon as it is possible. Right now there are a limited number of slots, because processing all the feedback takes time away from development also. If you are interested in joining the closed beta test, you promise to keep it secret, you have an email+password login on your account (not Facebook/Google+/Twitter for right now), you're playing on Windows, MacOS, or Linux, and you'd find it interesting to play on a feature-incomplete system, please message me this info: your name, your email, your Dominion Online login (if different from your email), your Making Fun forum name (create one if you don't have it), and what OS you are on. I'll add the first 25 complete replies.
Or you could just wait, because in a couple weeks we'll open up the beta for everybody to test. :-)
Right now we are only testing Windows, MacOS, and Linux native builds. We'll start focusing on finalizing the web builds in mid-June and then move on to finalizing builds for tablets.