Is wide-gamut video primarily an increase in saturation (for the layperson)?
Wide Gamut color space is primarily just an expanded color space that is capable of covering a larger range of values in the visible color spectrum. This, compared to sRGB and Adobe RGB. 

The gamma and white / black points are roughly identical. 

So yes this is primarily what Wide Gamut is designed for. Higher levels of vibrance. 

The trade off is if the end user is viewing the material in an 8 bit environment, gradients can appear a bit posterized. Wide Gamut is designed to be used and viewed under 16 bit or higher colorspaces.