These are the main notes I managed to translate from the video in French:
-Vatican City-Monaco was the only match played by the Monaco National team in this season.
-The Monégasque Football Association receives €9,000 per season.
-The players eligible for the National team are: Monégasque citizens, men married with Monégasque women and sons of Monégasques.
-The coach is Thierry Petit, the son of the former French international Jean Petit.
-The president of the Monégasque FA is Éric Fissore, nicknamed "The Monument".
-Their most prestigious result was a 2-2 draw against Gibraltar.
-Before that game, Monaco had already faced Vatican 5 times.
-The friendly was played in Rome, at "Campo Cardinale F. Spellman", on 29-04-2017 and the result was 0-0. Monaco didn't use the traditional red and white kit, but employed a the white and sky blue kit. The level was very far from the professional standards...
I've also contacted some members of the Vatican and Monégasque football organizations in order to get additional details. If I manage to get additional info, I'll post them.