The effect of increasing pressure and two-dimensional (2D) confinement on the dynamics of glass-forming polymer poly(methylphenylsiloxane) (PMPS) was investigated with the use of dielectric spectroscopy. We demonstrate that the glass-forming polymer confined to nanoporous alumina might obey the density scaling relation similar to that in the bulk and that the same value of the scaling exponent is used to superimpose the alpha-relaxation time measured under different thermodynamic conditions. Our comprehensive analysis of the relaxation processes detected in the dielectric loss spectra of PMPS allows us to identify the Johari-Goldstein beta-relaxation which for a bulk polymer shows up as a well-resolved peak while under 2D nanoconfinement only as an excess wing. In contrast to previous studies, we provide dielectric evidence of an additional alpha'-relaxation, slower than the segmental (alpha-) dynamics, which is related to the chain dynamics of PMPS.