Electronic – Does a twisted pair cable radiate more EM radiation than non-twisted pair

When you say signal is tied to the shield, which pins? The ground pins are tied to the shield. See pinout below

I am surprised to see that the grounds of the vga cable are tied to the shield, on the cables I have some of the grounds are tied to the shield. This is a more noisy solution, but with the cable making industry its about what works not what is best. They may be cutting corners by eliminating some conductors in the cable and running the ground through the shield.

A shielding conductor is used to prevent electrical fields to capacitively couple to the conductor they are protecting.

As far as turning the cable into an antenna:

From the cable shielding wiki:

The best method to wire shielded cables for screening is to ground the shield at ONE end of the cable

This is to avoid ground loops, ground loops are a big problem because current flowing through the cable causes current through the shield conductor to couple to the signals inside the cable magnetically. So to prevent this current flowing on the outside of the cable a choke can be placed on the outside of the shield to increase the high frequency impedance of the cable and cause high frequency signals to find a different "pathway" (as high frequency currents will "prefer" the path of lowest impedance/inductance).

The cable is shield is probably not tied to ground on both ends (computer and monitor sides), and one would hope that it is isolated somehow. Otherwise DC and AC currents will flow through the cable and cause problems.

So the shield shouldn't be tied to ground, it is probably introducing noise but it is and it still works, as far as we can tell. It would be interesting to find the VGA specs and see if this is a standard practice.

Ok I've been in the industry for years, and build signal power and video cables daily. Use tinned copper overbraid. Each shielded cable inside should have the shield exposed and stranded together so you can solder the shields to the overbraid. Then the answer lies in what type of connector you are using. I would typically unstrand the overbraid and lay it all the way around the back shell then heatshrink tubing over the overbraid and backshell. Heat very high, like 850-900, this will cause the 'tin' to flow and create a nice shielded cable. All signals shielded from one another and the entire cable shielded as well. Remember...do this on BOTH termination ends