The WiiU actually does this. You can play games on the 'iPad'-esque controller while some TV show (or whatever) plays on the TV.
But the WiiU is not scoring well with the 'core' gaming market. I am one of those young adults in a single apartment with a PS3, Xbox 360, and PS2 hooked up to my tv. I also have an old Xbox running XBMC in my bedroom. And there's a few reasons why the steambox/wiiU/appleplayer aren't appealing to me and quite a few of the other 'core' gamers I talk to.
The steambox (from the specs semi-released) are:
Between 4 and 8 gigabytes of DDR3 RAM
A quad-core 64-bit, x86-based 32nm processor running at up to 3.2GHz (with 4MB of Level2 Cache)
An integrated graphics card containing up to 384 programmable cores
That's just a computer. And a $999 one at that. There is a cheaper $499 option, but anyone who is interested in knowing the specs that they need to play (ie, tier 1 steambox vs tier 2) will just build a computer and hook it up to their tv with Steam's new 'Big Picture Mode.' There's no reason to buy a steambox; if you use Steam, you already have a computer.
The WiiU has the same problems as the Wii1. I know the Wii was the best selling console of the three big ones, but it didn't appeal to the 'core' segment for the simple reason that it had no good games. Sure it had a Zelda or two and a few Mario's, and a lot of people bought a Wii for those games. But that's it. After you play those games the Wii collects dust. Now that's not a problem for Nintendo because they didn't really sell the console at a loss (like most companies do). But if anyone else tried that it would be a bad idea.
But the WiiU does have your handheld idea. Which is actually really cool. But this comes at the cost of battery power (like you said), since even the tablet/controller can only last 4 hours without a charge. It also comes at a cost to graphics, since streaming content in real time to a tablet is rough. Most games already lag at 100 ms (fast action games are ~60 ms), and adding much more will kill the game, so they scale down the pixels. So for the 'core' market that buys all the $60 AAA titles, they want more, and the Wii can't deliver. When a game came out on all three systems (360, ps3, Wii), the Wii was by far the worst one. It had less power, worse controls, and a terrible online system. Obviously I cannot speak for the future of the WiiU, but I imagine something similar when the new Xbox and Playstations come around.
Now as for the biggest threat being Apple? I've never heard this before and it seems quite silly. But this really sticks out:
'Well, I could buy a console, which assumes I'll re-buy all my content, have a completely different video system, and, oh, I have a completely different group of friends, apparently. Or I can just extend everything I love about the PC and the internet into the living room.'
The people who will buy games and consoles don't think this. Or if they do it's as easy as plugging in a cord to your tv, with the added benefit of not having an iOS system. Which I assume would be heavily locked down similar to the iPhone, iPad, and iPod. If Apple enters the market they will have all the people who play the $1 games. The so-called 'casual' players. And if that's what Gabe is after, more power to him. But he is the creator of Half-Life, Portal, Team Fortress 2, and the most popular game delivery system on the PC (and linux!). The future of gaming does of course involve both types of players, and the 'casual' market is probably bigger than the 'core' market. But the 'casual' players don't buy $500+ machines made for the sole purpose of playing games.
Apple might overtake Microsoft, Sony, and Nintendo in terms of dollars if they want to, but that doesn't at all mean any lost Xbox, Playstation (or Wii!) sales. So I don't think the future of gaming is in any risk.