If it receives anything but ICMP packets, it breaks miserably. This should have just been called a tiny ping responder program. (And it can't deal with any problems or normal network issues at all even to do that.) It has no relation to an IP stack other than it reading network data raw.
It is not a toy stack, because it is not a stack. Toy or otherwise.
This does not merely lack completeness. This is an entirely different project that has nothing to do with making an IP stack. It does not even do the first thing an IP stack might do.
I do not get to claim my side project making a compact sandwich is a restaurant either. The author is making sandwiches and should be proud of that because a good sandwich is a great thing, the author should not be telling us he has built a restaurant.
While the tweeted 'stack' only responds to pings the other work by sics in general and Adam Dunkels in particular is very interesting. I've ran their Contiki OS and uip stack on a atmega8 microcontroller that had 8 kB of Flash and 1 kB of SRAM. If you are into tiny or embedded operating systems and network stacks I highly recommend taking a look at Contiki.
An IP stack has to expose basic IP functionality, not just responding to pings. Can it, for e.g., do IP forwarding? (that would be an awesome full fledged router) IP checksums?
Also, this program is vulnerable to the classic Ping of Death attack. ;)