I'm not sure the terminology "protocol" vs "non-protocol" is really the most accurate. Cygnet has protocols and procedures under which it is used, for example.
Similarly, NeurOptimal internally, uses parameters and algorithms to fine tune the process of their sessions.
There is such a wide range of neurofeedback software. I think what the NeurOptimal site you first mentioned was trying to get at is -- does the software reward or inhibit certain types of brain activity. Or does it just report back to the brain / CNS it's current state, and let the system as a whole have the intelligence to self correct and guide itself into a more stabile, resilient state? I've seen the term non-volitional vs volitional applied in this context,
Your statement, "The idea of stimulating the brain repetitively does give me scare for side effects. Is this a legitimate concern?". 'Stimulation' is not the right word to use here. Perhaps you picked that up from the article you linked to. Traditional neurofeedback is using a reward / inhibit paradigm, similar to operant conditioning, but at lower levels. There is no conscious operant process, the brain is learning new ways of self organization.
There are brain stimulation technologies, in fact a whole field of them. But neurofeedback is not considered stimulation.