The sizing of monitors in inches really has nothing to do with anything. It's instead all about the resolution being fed into the monitor. So while the monitor might be advertised as 19 inch, the more important measurements are things like aspect ratio (4x3 or 16x9) and pixels. Common pixel dimensions are 640x480, 1024x768, 1280x720 (720p) and 1920x1080 (1080p).
SnagIt captured images seem to just "work" right out of the box with things. So no real need to ensure proper DPI to make them work.
You might find the linked article to be of use.