Is unplugging computer power cable from PSU the same as electricity outage?

Motherboard electrolytic capacitors don't last forever. They were 13 years old already and degrading so they had just degraded beyond the level that the motherboard will not work any more. The power outage happening few days before motherbord failure is unlikely to have had a significant role.

The end is the same, power cut, but the transient behaviour (namely voltages) may be quite different.

In a power cut probably voltage would go down, because of the fault causing the power outage and then go to zero, thus having less impact on you. Of course this is the case if the power outage is a "relative" big one.

If the fault on the electrical transmission or distributionn network happens relatively near to you, for instance lighting hitting a power line, then your electrical installation and your PC could suffer from high transient voltage, which are dangerous for electronics.

Now back to the "pulling the cord", this could theoretically cause sparks (and thus high transient voltages.) This could also happen with a normal manual switch which though is normally not used to switch off brutally.

At any rate, the components impacted would be in the power supply unit, as it's there that 12V-5V are "produced" and fed to the motherboard. Also in my opinion the PSU normally protects other components and in worst case fries itself, but overvoltages are attenuated before impacting 12-5V components.

So sorry, no logical explanation for me.