This isn't actually a Construct 2 bug - it's because Chrome now requires HTTPS support to allow fullscreen mode. Chrome makes a special exception for localhost, but LAN IPs don't qualify. You can work around it using Chrome dev tools and a wired connection with port forwarding, which means you get a localhost address on the device too, but it takes a bit of setup.
This is a freaking disaster! So in other words, Preview on LAN is now worthless.
So now we have to export every time we have to preview on mobile, this makes things a hundred times harder.
I guess C3's mobile support is a great idea after all.
But more of C2's features is depreciating as time passes.