Are computer games (such as car racing or strategy games) permissible or forbidden, and does the Prophet's ﷺ race with Aisha (may Allah be pleased with her) make physical games permissible, as well as mental games?

There is no harm in electronic, physical, and mental games, so long as they are free from شرعي (Shari'i) prohibitions, such as the display of 'awrat (private parts), music, and distraction from duties. The Prophet's ﷺ race with 'Aishah is ثابتة (established) and صحيحة (authentic).