The performance of non-iterative soft demodulation for coded modulation schemes based on the serial concatenation of a low-density parity check (LDPC) code and differentially encoded (DE) quadrature phase shift keying (QPSK) modulation in presence of phase noise is considered. Transmission takes place over an additive white Gaussian noise channel in the presence of a multiplicative phase noise that is modelled as a random-walk (Wiener) process. For the considered non-iterative soft demodulation approach metric computation for the decoder is done as if the received carrier phase were perfectly known by using only two successive samples of the received signal. Numerical results, obtained with a near-Shannon limit LDPC code, show that the performance achieved by the non-iterative demodulation method is slightly worse than that of the more complex iterative scheme based on the Tikhonov parametrization for two values of the phase noise linewidth that are of practical interest.