Most sites I have visited reading on this interesting topic state something along the lines
"the only powers of two (other than 2 itself) that occur in this sequence are those with prime exponent" (MathWorld)
"After 2, this sequence contains the following powers of 2: [...] which are the prime powers of 2." (Wikipedia)
These careful formulations would imply that the set of powers of 2 generated in the sequence is a subset of prime powers of 2.
However, the OEIS seems absolutely certain that the two sets are equal: http://oeis.org/A034785
This result is also cited on other sites I do not consider very reliable for exact wording, like http://esolangs.org/wiki/Fractran.
Honestly, I have not understood the internal mechanics of PRIMEGAME enough to answer my own question yet. However, I think it makes a significant difference in the interestingness of PRIMEGAME. Why would sites like MathWorld not state the full fact?