Any pseudorandom stream generator is periodic, with the period at best proportional to 2^n, where n is the number of bits in the internal state of the generator. But you're right that the period in the example seems way too small. A correctly chosen 32-bit linear-feedback shift register (LFSR), would have a period of 2^32 (about 4 billion), which would be hard to see.

Yeah, you can see it has a small period from the presence of a repeated pattern. I think if he had used the Mersenne twister algorithm the output would be indistinguishable.