So, if someone don't have means to spread his LAN cable from the router to the distant PS4, he wont be able to play MP games when RP is active. Because of this, I've added "Use LAN cabble" in Direct Connection image in OP.
When someone confirms that only 1 WiFi connection is possible [either Internet or RP], I will add more clear text into OP.
This came up in a
previous post about Remote Play and I think where we got was that we don't know how capable PS4 is, but router technology has come a significant way since PS3 launched. (But also, PS3 can do some simultaneous local and networked functions; I just tried my PS3-to-Vita and it allows me to see my PSN friends list and messages but did not allow me to browse PSN store.) A modern router or network card will carry support for something like WiFi Direct or have some other plan for allowing multiple simultaneous connections. Here's some info on the WiFi Alliance's version of the technology:
http://www.wi-fi.org/download.php?f...oads-public/faq_20101021_Wi-Fi_Direct_FAQ.pdf
The problem we have now is that we don't know how powerful the PS4's router is. Sony has not confirmed the PS4 to be WiFi Direct-enabled machine (not that this makes or breaks the power, WiFi Direct is a certification rather than a special chip.) Until we know that (or until Sony addresses the range of possibilities,) we won't know what the PS4 can and cannot do in Remote Play that PS3 could not. That said, it feels like it'd be foolish for Sony to allow a bottleneck in this aspect of the system.
Curiously, of the two, Xbox One has announced that its online system uses WiFi Direct (its controllers actually connect to the box through WiFi rather than Bluetooth, although that still doesn't explain why PS4 only supports 4 controllers when PS3 was also BT and did 7 players.) It is not a feature listed in the PS4 specs, which are thus far very limited as it is .I have not seen Sony comment or been asked to confirm/deny WiFi Direct integration (might be worth an ask?)
Wii U also uses WiFi Direct for its GamePad sharing (weird, I always thought it was some custom signal like what DS had for its local play, but whatever.) And they seem to be pretty happy with the results there...
FYI, you can actually buy a mouse for your home PC that connects via WiFi instead of BT or a USB peripheral.