Theres no difference between a DVI video connection, and HDMI video connection.
In terms of Video quality, they are the same.
The only difference is HDMI carries audio as well.
So, if theres no particular need for the Video and Audio to be carried by the same cable, DVI will look identical to HDMI on your PC monitor.
This is why it most likely shows it as connected to a TV, as thats the most common use.