JinKazaragi: It isn't very wierd, just imagine how long the demo would've been if they backtracked after every battle to get all the items (especially since they obviously used some kind of Dev-mode which made that unnecessary).
Gekko_Dekko: It wasnt weird, if they used to loot atleast few enemies, to show how it works. Instead - I've got a feeling that it will be more "shooter with RPG elements", than "rpg with shooting" (in said context). E.g something around new shadow warriors, rather than, dunno, "witcher with guns"
Even with the complete lack of it, it still isn't wierd.
I don't think that this prensentation was intended to be shown to the public (it's the very same part which was shown at the E3 behind closed doors) and only was released because of the high demand for gameplay footage.
The jounalists weren't allowed to make video or audio recordings, because of that they have to keep track on the important part as good as possible and don't look at most of the details. So if it's ignored anyway, why showing it.
There's also the possibility that the inventory still is too bug-ridden/incomplete to be shown yet or they already intend to fully redesign it for some reason, it's a very early build of the game after all. (Why showing something that either isn't finished far enough to properly work or is already known to be entirely different)