What is the ruling on the prayer of one who entered the mosque during the second rak'ah of the 'Isha prayer and prayed with the intention of 'Isha, though he had not prayed Maghrib, then made up the Maghrib prayer afterwards?

What you did is correct, Allah willing, and it is in accordance with the view of the majority of scholars. There is no need to repeat the 'Ishā' prayer after performing Maghrib. The opinion that you pray with them with the intention of Maghrib has been stated by some scholars, but what was mentioned (i.e., not repeating 'Ishā') is more cautious.