pretty sure this is a form of post processing and can't be done on the fly in real gameplay
without a shader mod installed

You might be able to somewhat replicate it using Digital Vibrance.

Its a color correction in sony vegas or something

Most likely just color correction using "color corrector" in sv but could also be magic bullet looks for sony vegas/ ae. Never heard of anyone actually modifying in-game colors but the prior sentence is just what I know on what you see in the video

a lot of frag-movie channels do heaps of post-recording work to make everything look more shiny or colorful. There was some program specifically for TF2 demos that adds a new skybox, adjusts the contrast/colors, ETC and then records it (since it's post-game it can handle a lot more intensive stuff), but I can't remember for the life of me what that program is called. I'm sure he probably did some vegas pro/premier touchups too.

You could always experiment with high quality configs or just maxxing out ingame settings, but I think the answer you're looking for is probably not something specifically applicable to ingame.

I tried to create a similar sweetfx color correction preset
Screenshots http://imgur.com/a/4pFIO
It won't get you vac banned a lot of people have used this mod in counter strike and i myself in tf2 for about 8 months but it isn't allowed in ESEA and might get you banned from there, don't know about other leagues though.
here's the download
Extract the zip in X:\SteamLibrary\SteamApps\common\Team Fortress 2 and disable in game Anti-aliasing or it wont work press scroll-lock to toggle the mod on/off and if you want a more bluer tint open SweetFX_settings.txt look for Lift Gamma Gain settings section and change

#define RGB_Gamma float3(1.000, 1.000, 1.030)
to
#define RGB_Gamma float3(1.000, 1.000, 1.060)

Or a higher value you can also you use VibranceGUI for kinda similar colors