That is just running the TCP/IP layer speaking RS232 and relying on an external IC for lower layers. It's not at all what the GP is looking for.
It should probably also be noted that a minimum TCP header, with no data attached, is 20 bytes, so to implement a 'full stack' in 68 bytes is a pretty strong indication that you're relying on off SoC memory to handle the packet buffering.
From the first line of the source, it's a PIC (microcontroller) program, rather than something for x86 (which VirtualBox and friends emulate), so, no.
There are a few open source PIC simulators -- e.g. [1] -- and I would guess you might be able to get it running, since the link layer is SLIP over a serial port. You'd just have to wire up the simulator's serial console in the right way.
http://www.kyllikki.org/hardware/wwwpic2/src/wwwpic2.asm.htm...
Bonus: runs on 68 bytes of ram. Not a typo, it's bytes, and it's a "complete" http+tcp/ip server.