How is this interpreted by PostgreSQL?
The documentation tells you:


  A joined table is a table derived from two other (real or derived) tables according to the rules of the particular join type. Inner, outer, and cross-joins are available. The general syntax of a joined table is

T1 join_type T2 [ join_condition ]

  
  Joins of all types can be chained together, or nested: either or both T1 and T2 can be joined tables. Parentheses can be used around JOIN clauses to control the join order. In the absence of parentheses, JOIN clauses nest left-to-right.


The only way to parse the expression

a JOIN b JOIN c ON cond2 ON cond1


that is in line with the above syntax is

a JOIN (b JOIN c ON cond2) ON cond1


so if your code doesn't throw a syntax error, that's how it must be interpreted.