Every material is a conductor in a high enough potential! And if you pass enough current through copper, it can get to the same temperature, provided you're careful enough to maintain contact after it melts.
The distinguishing feature to call these "conductive" is that you could make a kiln of these bricks and ordinary bricks, and the current should preferentially pass through the conductive ones. Some of the current will leak through every other available path, including the air, but that's true of every circuit in existence. Vacuum isn't supposed to conduct, but vacuum tubes pass current through it, don't they?
Yeah, but how do you make a copper wire heat up without also heating up the wiring that leads to that copper wire? You can make it thinner, but these bricks aren't very thin.
Induce a current magnetically and you don’t need a direct wire connection. As for what to put in the intervening space I will leave that as an exercise.
Induction cooktops are ridiculously efficient at heating
You've probably seen multiple instances of this in your daily experience. A fuse is a thin conductor between thick electrodes. A light bulb is a very fine conductor between thick electrodes, encapsulated in a vacuum bulb. If you use tungsten electrodes, you can easily melt copper in the manner I've described -- that's how TIG welders work.
Responding to your question about electric current:
Quite simply, use leverage! Take a transformer with multiple (N) windings on the primary and a single winding on the secondary. Putting one (DC) amp through the primary will induce N amps through the secondary. With induction, you can use a low current to induce high current. Or correspondingly, transform low (AC) voltage to high voltage -- this is how high voltage power lines work.
True, but something should be there to close the loop on that not-so-thin brick, and that something will get hot. That picture shows only a single brick, not a loop of bricks so something does not add up.
You stick a large high temperature electrode into molten copper. This is how an arc furnace works. Some have water cooled electrodes to keep them from melting.
There is a difference between thermal conductivity and electrical conductivity of a material. They have low electric conductivity, so when you try to pass a current through them, they get hot. They are thermally conductive, so the heat spreads around the brick quickly.
The distinguishing feature to call these "conductive" is that you could make a kiln of these bricks and ordinary bricks, and the current should preferentially pass through the conductive ones. Some of the current will leak through every other available path, including the air, but that's true of every circuit in existence. Vacuum isn't supposed to conduct, but vacuum tubes pass current through it, don't they?