A question about electronic measurement of pulsed laser
I have read recently somewhere which I cannot find now, that extreme short pulse width lasers cannot be generated electronically.

That is correct, for femtosecond and shorter pulses, techniques such as mode-locking are used to generate pulsed output.
In mode-locking, nonlinearity in the laser itself is used to spontaneously generate pulsing.

But if electronic circuitry is not capable to to generate such laser pulses, how is the pulse width of them measured and recorded by a device(which is also made up of electronics)?

Pulse width of short lasers is most often measured using an autocorrelator, where the pulse is compared to a time-delayed version of itself using a nonlinear medium.  See optical autocorrelation.