Block difficulty is adjusted so that blocks occur on average every 10 minutes.

10 minutes X 210,000 blocks = 2,100,000 minutes.

2,100,000 minutes / 1,440 minutes per day = 1458.333 days.

1458.3333 days / 365.242 days per year = 3.99 years.

It looks to me like he started by deciding that the block reward would be cut in half every 4 years, and then calculated that out to discover it would be 210,379.392 blocks.  Then he probably just rounded off to 210,000.

As far as I can tell, the unexplained magic constants in the bitcoin protocol are:

• Starting subsidy of 5,000,000,000 integer units
• A Bitcoin defined as 100,000,000 integer units
• Subsidy reduced by bit shift (essentially divide by 2 and round down to nearest integer unit)
• Subsidy reduced every 4 years, rounded to be exactly 210,000 blocks
• Difficulty adjusted every 2 weeks (2016 blocks)
• Difficulty adjusted for average 10 minutes per block

I see a lot of numbers in there, but not many 21s.