You're confusing an adapter with a converter (these are two different things)
Most projectors and some HDTVs are built cheap and to reduce parts they accept component over a vga port. The adapter (usually included) doesn't actually convert the signal to VGA it simply feeds the Component signal to certain pins in the VGA connector and the circuit in the TV can determine if it's a component or VGA signal that it's receiving and treat it appropriately.
All these adapters do is change the shape of the connector, they don't have any circuitry to modify the signal and thus it's still component just with a different shape connector.
These will never work with PC monitors because PC monitors don't understand component video signals regardless of the shape of the connector.
Converters also known as "transcoders" which is what I'm recommending here. these will actually modify the component video signal and convert it to a VGA signal which in turn can work with any PC monitor or VGA capable HDTV.
A good rule is... if you don't have to plug it in... it's not converting/transcoding anything. Conversion circuits require power, standard video cables don't contain power sources so anything that's doing conversion will require either batteries or plug into the wall.
if you're not plugging it in then all it's doing is changing the shape of the connector.