Violist:
Yes and no.
Technically, RAW, the ape's need Improved Unarmed Strike before they can take Improved Grapple.
However, the basic feats assume one of the core races; Improved Unarmed Strike lets you deal lethal damage without provoking when unarmed. With their natural claw attacks, the Apes can deal lethal damage without provoking when unarmed. Null has quite reasonably ruled that the particular technically required feat won't be enforced.