Those small adaptors only forward the video signal that is coming @ 31kHz from Amiga side. And you can only do that when you're in Workbench and using the Monitor drivers which suit to these. Like DBLPAL/DBLNTSC, Euro36, Super72 etc. But Amiga PAL/NTSC output is 15kHz and PC monitors commonly use 30kHz. Some Multisync monitors support 15kHz too.
Many (old) Amiga games want PAL/NTSC screen. So you need a Scandoubler/Flickerfixer. A simple VGA adaptor won't work :-(