Have to agree with the most common argument here - military rank is not common knowledge at all. Not even for the populace of the countries that use them.
At best, you can argue people kinda understand the concept of captain (someone who has a larger number of men under his arm), admiral (controls big naval army) and general (controls big land army). And that's also mostly skewed from popular media (because that's how most get their knowledge).
So yeah, neither common (in its naming scheme), nor common knowledge.
The "material" badges are common place in a lot of games to represent competitive rank. I'm sure 95% of the children populace would sooner understand if you told them you were "diamond" rank rather than "corporal" or whatever.
Also, as already mentioned, there's not only 3 tiers (bronze, silver, gold) to the FAF's ranking system, there's 6 (bronze, silver, gold, diamond, master, grandmaster).
Most games have ties to the Elo system, which, although not used by FAF, is the most prominent and actually well known system to rank competitive mastery. And it has its roots in chess, from which the "master" and "grandmaster" titles are derived from.