This famous picture shows the where a thermite shaped-charge was used (over confused fireman's head) to ‘walk’ this column in our direction part of the typical Controlled Demolition process.
A 'thermite shaped-charge'?
Shaped charges are explosives molded into special shapes (roughly conical shapes or long V shapes) with detonators at one or more key locations, plus a liner of material (often copper) which will be explosively formed into a plasma jet during the detonation. The expanding shock wave from the explosive material compresses, superheats, and accelerates the liner, transforming it into a plasma moving at hypersonic speeds.
The geometry of the shock wave in a conical shaped charge forms the liner into a jet moving along the cone's axis. Linear shaped charges project a bar of plasma parallel to the charge. This high velocity plasma can cut through metal and other substances. Conical shaped charges are used to penetrate substantial thicknesses of metal, as seen in antitank weapons. Linear shaped charges are typically used in building demolition; careful placement of one or more pieces of linear shaped charge around a structural member will cleanly cut it when the charge is detonated.
Thermite, on the other hand...
The reason the phrase you used is so ridiculous is that thermite is not an explosive. I've seen thermite burn, at close range (maybe 20 feet away). (Well, I didn't look directly at it: no welding goggles to protect my eyes from the UV, so I looked away when the demonstrator lit it off.) It burns very energetically, at extremely high temperatures... but an explosive it is not. 'Thermite shaped charge' is an oxymoron, a complete contradiction in terms. There is no way to get the carefully controlled detonation required by a shaped charge out of thermite, because it doesn't even detonate.
For the purposes of demolition, thermite is an alternative to shaped charges, not a component in shaped charges. It isn't a very good alternative for controlled demolition of buildings, however: it's prone to setting fires, melts itself, burns so hot it's difficult to contain, and is just generally difficult to control.
Thermite's properties do lend it to some demolition applications. For example, it's great for destroying the usefulness of military equipment without requiring an explosion. Set off some thermite on top of an engine block, and as it burns it'll melt a hole straight down through the block. It can also be used to disable or destroy artillery pieces, and was used in incendiary bombs in WWII (thermite can't be smothered and burns hot enough to ignite everything you'd be interested in igniting with an incendiary bomb, so it is excellent at starting fires).
Sometimes thermite is even used for low quality welding: it'll produce enough heat to melt itself and the work surfaces, and if you use iron oxide as the oxidizer the thermite reaction generates molten iron. Carefully control the quantity of thermite and it'll make a weld instead of destroying the pieces you want to weld.
But if you want to demolish a building, not so good. Thermite is a great way of generating a lot of heat and molten metal. But it's hard to harness molten metal to perform a controlled demolition. For example, it'd be very, very difficult to produce that nice, clean angled cut in your picture with a thermite reaction. And there's no way thermite is ever as quick and clean as a shaped charge when it comes to cutting a support column.
Note that 75 percent of the molten metal residue fell ‘outside’ with only 25 percent on the ‘inside.’ That is a classic CD signature where powerful shaped charges are utilized, because the initial burn starts from the outside and works quickly inside the column.
Uh, no. Classic CD signatures have no substantial amounts of molten metal residue at all, becuase very little metal exists in a molten phase during the detonation and subsequent aftermath of a shaped charge. The plasma jet is arguably molten, though technically plasma is a different phase of matter from liquid. And some of the metal hit by the plasma jet of a shaped charge is temporarily liquified. But it's a very brief event, and only a tiny percentage of the material in a girder cut by a shaped charge is ever liquified (that which is directly impacted by the plasma).
I've seen photographs of tanks penetrated by shaped charge weapons. From the outside, usually all you'll see is a tiny clean hole with some blast soot around it, the hole being no larger in diameter than the plasma jet projected by the shaped charge. You don't see huge amounts of molten material anywhere.
All the columns above this one were ‘severed’ moments earlier, until this one burned and allowed the entire column line to ‘drop’ and literally break the back all the way up the line.
Your conception of how controlled demolitions are performed simply has no connection to reality.