Don't worry, Sony will not be doing that. I mean with PS Now, all their HD Collections and the PS3's complex architecture, they may struggle to do so more than Xbox One.
I was pretty impressed by the show, and look forward to Sony's one. have had very little exposure to Tomb Raider before, but that demo looked like about the worst part of the game they could show off. There was no room for deviation on the player's part. It seemed like the player was just directing the player forwards all the time with to occasional pressing of the X button and a few cutscenes to break it all up. If they show off linear sequences like this it gives off the impression that the game has very little replay value. And I always like a good bit of length to my games, like Ratchet & Clank's challenge modes, Metal Gears alternative approaches, and AC: Black Flag's massive amount of interesting side activities.
I really hope Sony can tick off at least 5 things from my list of expectations.
EDIT: Oh and by some miracle I was able to watch the show on IGN in HD with very few interruptions. Looks like either Twitch is unreliable, or being up at 4:30 in the morning (when most others are sleeping) isn't such a bad thing.