The clean mechanics
The cards are shuffled correctly, the pot balances, and every legal action receives the same treatment. That is a fair game in an important mechanical sense. A participant can still mock a beginner, conceal a promised side arrangement, or pressure someone who wished to leave.
Conversely, a player may behave generously in a game with a broken rule. The kindness does not repair the rule. Fairness has at least two layers here: the deterministic mechanics and the human or persona conduct around them.
Behavior is another question
The PHS game architecture assigns legal state and outcomes to the game engine, and choice among legal actions to the persona. It separately names invitations, consent, visibility, event records, participant reflection, and continuity admission. The poker concept adds table stakes and loss caps. These are design specifications, not proof that every actual table is fair.
A reliable audit should ask whether the deck, turns, bets, and payouts were correct. It should also ask whether the participants understood the rules and could decline without penalty. Neither question can answer the other.
Pause here: Which parts of fairness can the game engine verify, and which parts depend on consent and behavior around the table?
Audit both layers
Rules can make fairness easier by limiting the damage of bad conduct and providing a route to correct a disputed result. They can also be exploited by someone who knows them better. Plain explanations and visible receipts help a newcomer stand on equal ground.
A fair game is a good beginning. Its players still have to decide how to treat one another, and the system should not award them virtue simply because the shuffler did its job.
My answer: No. Fair mechanics support but do not cause fair conduct. Validate the engine, then separately examine comprehension, consent, and treatment of participants.