It's a matter of what we want to use for the unit of frequency. The result returned by the Welch function was a power density in units of $W/Hz$ (or more likely a power ratio or any other unit of power besides $W$). Specifically it is a a power spectral density as some unit of power over a 1 Hz bandwidth. This was set by the parameter `1/Ts` that was passed into the function assuming  `Ts` is in units of seconds. So in this case the code was created to instead plot the resulting power spectral density as power over a unit bandwidth in units of radians/sample.  

'(2 * pi / Fs)' converts units of Hz to normalized frequency in units of radians/sample. We often see this choice of units for frequency in digital signal processing and with it the DSP implementation can scale directly with the sampling rate (if we have a half-band filter for example, if we run it at twice the rate, it will still be a half-band filter). 

An example where such a translation would be useful in this case is if we had a filter or region of spectrum that was given in units of radians per sample, where the entire bandwidth is given as $B$. Then from the power spectral density mapped to the same frequency units as $S(f)$, we can easily compute the total power in that bandwidth as $S(f) B$ (assuming $S(f)$ is constant over $B$ otherwise this would involve an integral over $B$ or piecewise approximation).  

Below is a summary of the most common units used for representing the frequency domain. The top one is cycles/sec or Hz. If we scale that by the sampling rate, we get normalized frequency in cycles/sample. Notice how we have simply used a time index of samples instead of seconds. Also observe how the inverse of the sampling rate in Hz is seconds/sample (how much time for each sample). Thus if we divide Hz by the sampling rate we get (cycles/sec)/(sec/sample) which is cycles/sample.  We convert frequency in Hz to radian frequency by multiplying by $2\pi$ so similarly we can multiply normalized frequency in cycles/sample by $2\pi$ to get normalized frequency in radians/sample. Finally, as commonly used with the DFT, we can have a frequency index on $N$ samples typically abbreviated as $k$ with an index from $0$ to $N-1$. $N$ in this case would correspond to the sampling rate.  

[![frequency axis][1]][1]


  [1]: https://i.sstatic.net/bZB8tsfU.png