Ancient Technology
Answer: INSURRECTION
Zach Battleman, Kevin Zhou (Kaz)

This puzzle is about spoonerisms, such as "Dinosaurs" in relation to "Sino-doors". We identify the spoonerisms and then extract the switched letters. The numbers from 1 to 12 give an ordering for the extracted letters, which spells out the answer.

ClueAnswerExtractionNumbers
A hot coal is a referee at a dark brown kingdomEMBER UMPIRE, UMBER EMPIREE,U7,4
An acorn-shaped fastener had its short rest interruptedCAP NUT, NAP CUTC,N8,2
Math homework is typeset again by a large predatory dinosaurRETEX, T-REXR,T5,9
Power Sneakers or 1-Up is science, technology, etc. in a Greek dialectSONIC ITEM, IONIC STEMS,I3,1
Steel ingredient angers a nation with ancient Ekpu figuresIRON ORE, ORON IREI,O10,11
The top of a tree is a street named after Pingu's soundROOT NODE, NOOT ROADR,N6,12