Based on that observation further review of the logic board power and typically faulty components is required.
(Inadequate test wiring causes voltage drop from source to load, not excessive current).
OBSERVATION: Ah, that large power resistor in parallel with the LM323. 2ohm 20W. There's some good Arcade Classic Repair vids on this circuit. The resistor is there to help regulation and startup inrush. But I believe if there is a regulation issue, the LM323 should be doing alot of the work (regulating voltage and passing current) under normal conditions. (Though if you work thru Ohms Law and assume the input is 12V (10Vunreg), the output is 5V and the current is 2amps, then the regulator has an impedance of 3.5ohms and it and the resistor are sharing the load current and both are getting hot, but the regulator is less hot than if the resistor was absent from the circuit. This being said it is possible for the 5V circuit to operate at higher current than the rating of the LM323 since some of the load current is supplied by the parallel 20W resistor). Perhaps excessive power issue is occurring if either the resistor is out of spec AND/OR the LM323 is faulty. "Power and Connections"
Some more trivia. If using a 2amp 250VAC 3AG slow-blow fuse and noting that this fuse takes "20 seconds to open", this implies by the timing curve that almost 4amps is being drawn on the AC side.