Regarding the game business, it's not a good comparison. Selling games is like the DVD business: games are produced at a fixed cost and sold at nearly zero marginal cost. This is true of games sold on disc as well as games sold online through Steam.
But this is not how the movie streaming business works. Content is licensed, not sold. It's licensed to a single buyer for a fixed window of time. After that, it's licensed to someone else. This is why HBO, AMC, and Netflix will never be showing the same movie at the same time.
This is a profit maximization strategy by the studios. I doubt that major studios would make more profit with a direct to consumer model, at least not with one that would replace the windows in which Netflix typically buys content. It could potentially work for new releases, though. I'll leave the exact reasons why as an exercise to the reader.
I hope that Netflix's long term business model doesn't depend on the answer to that question being "No, that's not in their DNA."
It's nice that so many websites offer some kind of streaming video, but the friction of moving from site to site, each with their own navigation and search functions of varying quality, seems like as much trouble to most consumers as getting up and walking across the room to change channels on their TV.
Netflix has done a good job in aggregating content, although I don't believe they have a format and business model that is sustainable into the next decade.
Ultimately, the same Internet that will kill the cable companies will also kill Netflix. (I have more confidence in Netflix to reinvent itself when the time comes, of course, since you've already done it once.)