Transformer parameters surely affect transfer function. Could try S2SPICE tool to generate a realistic model.Turns ratio is 1:3 by the way, impedance ration 1:9.
Several circuit details look arbitrary and not well considered, e.g. the mentioned capacitors at transformer secondary. Effect is reduction of common mode suppression, depending on transformer parasitics and actual common mode noise. Also IF amplifier driving impedance is too high, adding out-of-band noise floor to log amplifier output.
All-in-all, I doubt that it's a good redesign template. Circuit behaviour should be nevertheless analyzed as a reference