There's a reason why the "alpha version" was "alpha" and it's nothing to do with maps or gameplay being different. Alpha versions are by definition unstable, short-lived, only work on a small range of computers, and very quickly superseded.
See http://en.wikipedia.org/wiki/Software_release_life_cycle#Alpha
The alpha phase of the release life cycle is the first phase to begin http://en.wikipedia.org/wiki/Software_testing ... Alpha software can be unstable and could cause crashes or data loss ...
If this version were to be officially released (presupposing that it even still exists on id's internal servers - which is one big "if") then it would need heavy work to bring it's engine up to full performance, compatibility and stability, not to mention a complete port of a second engine for PS3 and 360 (factor in another 8 months delay on BFG edition being released during which even less Doom 4 work would be done). Even with that there are most likely severe content bugs that need to be addressed. That's why alpha versions generally don't get released - this was not a "demo" as you understand it; this was a test build for internal use and showing off to selected third parties.
So just imagine, if it were to be released, the hoo-hah that would ensue when people try to max it out only to find that it doesn't even work on 60% of current hardware, and those that it does work on, it crashes with varying degrees of frequency. Nope, definitely file that one in the "not going to happen" pile. the best you can hope for is videos, and - well - you've already got that, haven't you?