What do gold medals on games in the plaza mean?

The most recent update (April 16th, 2015) to Streetpass added two new games, the Game Vault, and other upgrades. However, I don't recall anything in the Nintendo Direct video nor in any articles about the gold stars I now see on some of my games. In the picture, you can see that Find Mii I & II, Mii Force, and Flower Town all have gold stars next to them.

I so far haven't been able to find anything online about them. At first I thought it might be for finishing a game but I haven't finished Flower Town by far. I have finished the main campaigns of the other two games, but Mii Force isn't perfected.

What do the the gold medals on these games mean?

This community wiki answer will try to list circumstances in which people have or have not earned medals in an attempt to codify what's necessary for them.

For most of the sub-games, it is known that collecting all the related achivements is not necessary.

• Find Mii 1/2's medal seems to disappear if the player restarts a quest in order to collect hats. Therefore, it is not based on "have all hats". Odds are it means "has completed the (current) quest".
• Mii Force's medal does not require the player to have collected all gems or all titles, so it might mean "beat the game once".
• Flower Town's medal does not require the player to have completed all jobs. Likely to be based solely on earning the Master Gardener's Crown.
• Warrior's Way's medal remains even if the player starts a second quest. Therefore, it probably means "beat the game once".
• Monster Manor's medal remains even if the player starts a second quest. Therefore, it probably means "beat the game once".

Puzzle Swap is simple: If you have all the panels completed, you get the medal.

According to GameFAQs:

The medals are only to show you beat the main portion of that game.