How to tap out video signal from a computer or a TV
Computers have used many interfaces to send video information to a monitor.  Early in home computing, many used composite video.  However this had a bandwidth limit of about 4MHz for black and white and 3.8MH for color.  If you search through this patent you will come across some bandwidth limitations.  These are the types of signal the device you linked to is expecting.

Very soon, demand for both color and higher resolution obsoleted the composite approach which was replaced by CGA.  And that was replace by other formats like VGA.  And that was replace by other formats like HDMI which is digital.

While VGA is still analog, there are many incompatibilities between VGA and composite.  In a composite signal, color, brightness and video synchronization are all encoded into 1 signal. In a VGA cable, the colors Red, Green, Blue all have their own pairs of wires as well as the horizontal and vertical synchronization signals.  Also the scan rates are different.  Where as PAL and NTSC composite signals scan the screen at 50 and 60 times a second respectively.  VGA can scan up to 70 times a second.

Possibly the most incompatible difference is the number of dots that can be displayed.  As stated above a black and white composite signal display about 4 million dots per second.  That would be about (4,000,000 / 60) 67,000 dots per screen for an NTSC signal.  A VGA signal can put about 288,000 dots on a screen.

So, regardless of the effort or interface device, the resolution limit of a PAL or NTSC monitor will render certain applications (for example, reading 80 column text) impossible to implement.