Of course they matter, how can anyone say otherwise. Input/output impedance, input sensitivity, gain, number of channels, dimensions, operating voltage, number and type of inputs and color are all critical information. The information won't tell you how the amp will sound, but it will tell if it can operate properly in your system.
Amplifier specs, does they matter?
For solid state designs, the manufacturers boast about their signal to noise ratios, total harmonic distortions, slew rates, frequency responses, and many others. Meanwhile, the makers of the tube amps praise the liquidity and musicality of their designs. Obviously, amplifiers with tubes don't measure nearly as well as solid state amps. So, do any of these specifications really matter?