What is significant about the number 8069 ft?
Apparently you aren't the only person who wondered this; the FAA actually has it in an FAQ:


  What is the significance of a runway 8069 feet in length and why are two different aerodrome symbols used to depict hard surface runways on
  Sectional charts?  
  
  For purposes of airport depiction, specialists
  represent a runway between 7970 and 8069 feet in length as 8000 feet,
  which equates to a line 0.192 inches in length on the Sectional chart
  scale. In this case, a circular aerodrome symbol is used.  
  
  If a runway
  is between 8070 and 8169 feet in length, specialists round to 8100
  feet, which equates to a line 0.1944 inches in length on the sectional
  chart scale. This line is too long to fit into the largest circular
  aerodrome symbol FAA has available. Therefore, specialists place a
  line-work around the runway pattern forming a polygon (enclosed shape)
  for anything over 8069 feet in length.  
  
  Specialists also place these
  polygons around the runway pattern of aerodromes with multiple runways
  that are less than 8069 feet, in cases where the multiple runway
  pattern does not fit into the largest, circular aerodrome symbol.