That's not even close to my reading - a participant is simply one of team members in uniform that can participate in the game and the term even includes us (the officials on the field). One of 25-60 more or less per team plus the crew. He is not a substitute or a replaced player, those terms are explicitly defined as is the term player.
We're not splitting hairs here, we're going by the rules. Using the term participant in the context of the AR is simply illogical. If the AR means to say that when the PLAYER steps off the field and across the sideline into the team area that he becomes a DEPARTING PLAYER who must now stay out for at least one play (or a timeout period) it could very easily, and clearly say that using clearly defined terms from the definitions - it doesn't.
What it does say is that the player did not comply with the substitution rules, and given the specific set of facts in the AR (all of the facts) a flag is warranted, no more no less.