The security proof for Key Policy Attribute Based Encryption
Because the simulator picked   $\gamma$ to generate $g^\gamma$.  He acts as an ABE authority for an attacker who breaks the Selective Set Model security game so he can use the attacker to solve the   Decisional Bilinear Diffie-Hellman problem .

As a result of being  the ABE authority, the simulator  knows  the master secrets and all other secrets created by the ABE authority. Remember, that for normal ABE, the authority knows everything, including user's private keys (attributes).


  Proof: Suppose there exists a polynomial-time adversary A, that can attack our scheme
  in the Selective-Set model with advantage $\epsilon$. We build a simulator B that can play the Decisional BDH game with advantage $\frac{\epsilon}{2}$. The simulation proceeds as follows:
  
  We first let the challenger set the groups G1 and G2 with an efcient bilinear map, e
  and generator g. The challenger flips a fair binary coin $\mu$, outside of B's view. If $\mu$ = 0,
  the challenger sets $(A; B; C; Z) = (g^a, g^b, g^c, e(g, g)^{abc} )$ otherwise it sets 
  $(A; B, C,Z) =
(g^a, g^b,g^c, e(g, g)^z)$
   for random $a, b, c, z$. We assume the universe, $U$ is defined.


The simulator, then, gets to set up an ABE system so he can use the attacker


  The simulator B runs A. A chooses the set of attributes $\gamma$ it wishes to be challenged upon


$\gamma$ has nothing to do with the DBLDH assumption.