Prophoto is definitely a larger colour space that
can show more saturated colours, but only if those colours are there in the photo.Also saturated colours may not show up on your screen if your monitor color space isn't large enough to display it.
In general for any image, a larger colour space does not automatically equal more vibrant colours.
At first glance, the colours in your pictures are actually very bright and saturated already. The main reasons for the dull colours are,
1. The subject is slighty underexposed.
2. The colour balance is off, there's a blue cast across the entire photo. Could be due to the filter being used, wrong white balance or simply result of the post processing.
I tried removing the blue cast and the result is the second photo (right) below. Compare with the original photo (left)and you can see that the blue cast was interfering with the skintones and shirt colours.
Edit 1
However, by over-correcting, we lose the blue sky in the background, so I tried a rough selective correction for the skin tone and shirt as shown below.
Edit 2