How do I add text like this (picture) to a video? Can it be added post or is it an old camera function?
It was in camera function. But there is no such thing in video editing, which can not be accomplished with correct software.

You can add this text in Adobe Premiere, or Adobe After Effects with some noise etc... You can add it in almost any video editing software. Main thing you need — correct font. It is pixeelated all caps text. You can find one here: http://www.fontspace.com/category/pixelated

Next: Install that font in your system and add text. Make it all caps and with chosen font. Select color and for the second example you also will need black stroke.

Good luck!