The 21st century began on 2001-01-01.
Resolves mostly (see below for the exception) according to the Wiki page https://en.m.wikipedia.org/wiki/List_of_current_state_leaders_by_date_of_assumption_of_office and other sources confirming the person's birth date and other relevant information.
Except where otherwise stated, the criteria apply to the state of the world on the date the first such person comes into office as the leader of a sovereign state; this is the exception to the "follow Wikipedia" rule, because if somewhere right now there's a 5-year-old tribal king and they later become independent, Wiki will list them by the date of their accession to the throne and this market will refer to the date of Independence.
"Rule a country" just means "be associated with that country in the Wiki page, according to the criteria used by that page as of market creation"; rules lawyering about a given position not really being a "ruler" are null and void.
Members of constitutional ruling councils count for whatever role the council plays (head of government, head of state, or both). Coup junta members do not count unless they're the designated leader of the regime (but in any such cases, the Wiki page has the final word).
The United Arab Emirates is considered a federal monarchy for this market; the Emir of Abu Dhabi, who in practice holds the office of UAE President ex officio, does not count as President for this market. Royals like MBS and the Emir of Dubai do count as Prime Ministers, as that is their title and role.
However, the President of France does count as a monarch due to being Co-Prince of Andorra. Same for the other Co-Prince, the Bishop of Urgell. Their representatives, as well as Commonwealth Realm Governors-General, all count as royalty. So do underage monarchs with regents, regardless of the regent's age.
"Custody" means that, for any length of time, people exercising governmental (not parental) authority were preventing them from freely go where they wanted; Trump's brief trip to jail to have his mugshot taken would count, as well as being in jail or prison, Prince George of Wales being prevented by Prince William from running in front of a car wouldn't. Things like traffic stops and airport security checks do not count.
I may bet in this market. The only effect I can reasonably be expected to have on resolution is through my vote for President of Brazil, who, like in America, needs to be at least 35 years old.
New options are super welcome, but I don't commit to resolving them super quickly if they're obscure.
@HarrisonNathan excellent question, thank you. I'm not sure, but I lean towards this one resolving NO and the one about relatives resolving YES. North Korea doesn't officially consider itself a monarchy, and its propagandists point out the myriad meaningless positions the regime has - they try to portray themselves as not-an-autocracy. What do you think?
Ultimately, if that is the thing that happens first, I wouldn't totally reject N/A'ing this option, much as I generally dislike N/A's.
(Sh*t, this answer was nearly all typed here and I just hadn't hit send.)