Not sure I really follow that explanation, but the most basic uses of が and は are for introducing new information and identifying what both parties are aware of, respectively.
“Topic marker” is a label applied to は, but it’s basically a way of tagging something with “we both know about this already.”
When が is used, it’s signifying, “I’m bringing this into the discussion.”
It gets even more complicated because both が and は have more roles than just those… so you can have sentences with 2 が’s and no は’s, or the opposite. But one step at a time, I guess.
BTW, the reason you can say 私は when introducing yourself to a room full of people you don’t know is because presumably you’re already standing there and visible to them. They are aware of your presence, and so are you (obviously), so you’re already in the “we both know about this” category in a general sense, even if they don’t know any of the details about you yet.