What happened is, hot (supply) got shorted to Equipment Safety Ground, and caused massive electrical current (enough to do some welding). This current flowed through the dimmer. This killed the dimmer dead. It may have stuck in the "on" position.
Most likely the short was not the bulb proper, but rather, your changing the position of the socket so it was able to touch the metal chassis of the fixture.
The bigger problem is: shorting to Equipment Safety Ground shouldn't cause welding to happen. Looking at your lamp it's perfectly clear why: your safety ground is a chain. Chains don't conduct electricity reliably.
So while it's good to take the lamp apart and fix whatever the socket problem is -- it's much more urgent to fit a proper ground wire that runs up a chain (sorta like the power cord does). They make ground wires specifically for lamps, in a variety of hide-me colors.
Had the chain not carried the current, it would have instead electrified the fixture. This could have caused something analogous to an electrical drowning, where the electrical shock only stuns you and falling off the ladder breaks your neck (because you are not conscious to manage your fall).