There is no Sui Generis alpha yet. You likely saw the 'alpha gameplay' footage, but these were dev builds intended to show off the game. No one outside of the dev team has access to SG right now, and the devs' attention is squarely on finishing Exanima.
Yep, you're not missing out on anything . Everyone has equal access to the game except for insiders when they're testing new releases only for about a month before everyone else gets them., but trust me, it's not a job you want anyway hehe.