Relationship between height and depth of a binary tree
You're not missing anything: it's a typo, which I've fixed. The page gives two separate definitions of "full binary tree" (a recursive one and the one you quote) and both of them include the following trees, which have even fewer nodes than yours ($2n-1$, to be precise):

  o
 / \
o   o
   / \
  o   .
       .
        .
         \
          o
         / \
        o   o