From the iconography on the main page I'd guess the second announcement will be Steam hardware and the third one will be Half Life 3 (second circle indicates software product again?). Pure speculation on my side here.
Come to think of it, Dota2 just mentioned recently an update that either just came out or is coming out in a few days that would allow you to play a Dota2 LAN game. Perhaps the third announcement will be more along the lines of sharing a game only you own with friends on your LAN, for that sort of purpose?
Useless.
Two Steam OS added together. I think it means if you get two devices running steam you can combine them to increase the available resources for playing a game. Possibly some kind of build in clustering API that steam games can use.
If Half-Life 3 was represented it would have to be a sign inside the circle as it is mainly a singleplayer experience. Also a single game as a third announcement is way too narrow-minded as Valve already has the one of the most popular games (Dota 2).
I will be so Goddamn happy if they're actually making that thing. I love modularity, and a trackball gamepad would flawlessly combine the convenience of a gamepad with the precision of a mouse. Several groups have tried to bring one to market, and studies have shown their superiority, but apparently they were too weird to get enough preorders. Hope hope hope...
O = SteamOS
[O] = Hardware partners Steam box (in tiers inc. an inexpensive stream target box for $99)
[O O] = Being able to run a SteamOS game on your Windows system. Think DOSBox or HyperV.
If they could do this then really it's a case of convenience vs performance, and a few exclusives or two would push people to dual boot rather than VM it.
It could also be the way they plan to stream, i.e. a self-contained mini-OS that runs under Windows but streams out/in visual and inputs. The 'local' version fits ok with that, in that you can run a SteamOS title in Windows by localhost'ing it really.
Just speculating, but it's interesting to think about.