J-PAKE : About Schnorr NIZK proof for ephemeral private keys Reading J-PAKE Authenticated Key Exchange Without PKI document :
J-PAKE


  Round 1 : Alice sends out g^x1 and knowledge proof for x1, e.g :
      To prove the knowledge of the exponent for X = g^x1


My question is : Is then the recipient (the verifier) of g^x1 + NIZK of x1
    able to get the x1 value ?
No. The whole point of doing a zero knowledge proof (in this case, a non-interactive zero knowledge proof) is that the verifier does not learn any additional information besides the statement that is intended to be proved. 

The Schnorr protocol allows to prove knowledge of the discrete logarithm without revealing the exponent. On top of that, the Fiat-Shamir heuristic can be applied to the protocol to produce a non-interactive version of the proof, still without revealing the exponent.