The PS4 can do this because they designed it to sample the video internally with a video encoder. They can then stream that signal through the local network to a computer.
In theory you could buy an external device for a PS3 used to record via HDMI, and I'm sure there are some ways to get that working somehow. For the PS4 though, Sony is creating the software to make it easy to use.
You also get a lot of LATENCY issues through a network so games can feel sluggish, especially if using wi-fi not ethernet to connect the PS3/4 and PC to the router)
(to be clear, you're just using the laptop SCREEN and the PS3/4 is doing all the processing and streaming a video. Your button presses also go through the PC->network-> PS3/4)
The HDMI input thing not being there is true, however I suspect this was a question about gaming remotely from the PS3, and not connecting a cable directly to it in the same room.
So far, I can only find info related to a PS Vita which can play games natively, and SOME games on the PS3 remotely (not sure exactly how that works).
Obviously not what you want, but thought I'd mention it anyway.
*The only other thing i can think of which isn't very practical is getting an HDMI splitter, long HDMI cable (if even possible), and long USB cable.
A lot of issues getting this setup. A lot of people used to do this for connecting Gaming PC's to HDTV's. Then we got the STEAM LINK:
Unfortunately this doesn't support the PS3, though it's a software issue, not a hardware issue. In theory this could work, and in fact it's functionality is built into a PS4 and XBOX ONE anyway.
Again, you are STREAMING the video from the remote device through your local network to use the screen of some computer, then streaming back the button presses.
I hope this is informative, though it doesn't solve your issue.
Buying a PS4 would help, though two points:
a) XBOX ONE supports appears to be better so far (but requires Windows 10 which the PS4 does not)
b) PS4.5 is coming (rumor is it's a slightly faster CPU with perhaps 50% faster GPU... other functionality is uncertain)
c) upgraded XBOX ONE probably coming in the next year
If the XBOX ONE gets upgraded that's probably the way to go in terms of Windows 10 remote gaming.