The risk is that in some situations (it should not matter how often; the environment might be somewhat attacker-controlled) two processes produce identical random numbers. This is bad, because this breaks the assumption that random numbers are independent. A program may reasonably fork into two processes, one which uses random numbers to generate RSA keys and one which outputs random numbers to anyone who wants them. LibreSSL's flaw may allow these two processes to destroy each other's security guarantee.

Ahh, not really - while the process thing the author describes is real - what you're saying is that any two processes show the same values, and that isn't the case. the bad guy needs to control one process to read the values in a useful way, have it exit, and be able to maniuplate the system by killing or creating processes until his intended victim comes up on his selected PID. While that's far from impossible to do (just as the author's program does it) It is likely going to imply enough access to your system by the attacker that you're already pretty much p0wned.

An attacker doesn't necessarily need to know the random values themselves to pull off an attack. For example, if a nonce is re-used, an attacker might be able to decrypt data sniffed from the network. Also, creating processes to force a PID wraparound might be as simple as making repeated requests to a server.