I don't think the Chrome Cast is what you think it is. It cannot be used for gaming. It might work for web-browser games, but you are not going to be using it to play anything off Steam or play World of Warcraft on your TV. That's what I thought it was when they first announced it, but I was sadly mistaken. The Chrome Cast can stream stuff off of your Chrome Browser and that's pretty much the extent of it. It can run its own apps too like Netflix.
I've also looked into a wireless HDMI option, but right now those things are freaking expensive (more so than the Vita TV). The one at monoprice is $166.
The reason why I think the Vita TV works is because it has more processing power than the Chrome Cast since the Vita TV is essentially a Vita without a screen. The power of the other machine (in this case the Playstation 4) is also important for streaming from one device to another. The Vita has a 2Gz quad-core CPU and 512 MB of RAM. The Chrome Cast and even the Apple TV and Roku do not have that kind of power. Heck, the Roku 3 can barely run Angry Birds. I mean it can, just not very well because that's not what it was designed to do.,
I guess this device is for me because I am already pretty deep into the Playstation ecosystem and I have decided to get the Playstation 4 over the Xbox One due to all of Microsoft's ridiculousness. Playing the Playstation 4 in my office or in my kitchen without a second PS4 or moving a big console around the house is very appealing to me. I also have over 20 Vita/PSP games from my time in Playstation Plus, so it would be nice to actually be able to play them. One really big thing that appeals to me is that I love Valkyria Chronicles, so being able to play Valkyria Chronicles II on my TV with my Dual Shock just sounds awesome!
The Vita TV can also presumably run the streaming services from the PS4 that are not on the Vita, so that means I can watch MLB, NHL and WWE Pay Per Views using this thing. So yeah, while a $35 stick would be nice, it's probably not going to happen anytime soon. If Microsoft releases one for the Xbox One it will probably be $100 because such a device would probably have to have similar specs to the Vita or Nvidia Shield in order for it to work properly.
(I think why something like the Wii U Game Pad works is because they're using their own band and not standard wifi. Which means it has a pretty limited range of about 25 feet. I don't think a similar approach would work for streaming onto a home network)
When this thing launches here (I assume it's going to launch in the US), I think that they are going to have to include a controller and keep the $100 price tag. I mean, it's not a huge deal for me since I have multiple DS3s, but I just think it's going to be awkward for the consumer. I mean, you can get them for pretty cheap now, but the MSRP is still $54.99.