In a straight line, cars like the M135i and M140i will easily keep up with an E46 M3 and the latter probably convincingly beat them. But it's hardly a surprise is it? You give a car a turbocharger and get it kicking out masses of torque and bhp and couple that with an auto gearbox that has tight ratios and shifts nigh on instantaneously - of course it's going to go faster in a straight line. Even some fairly hard driving on the road would result in very similar results, timing wise. The E46 M3 will always feel more balanced, with a much nicer steering feel and razor sharp throttle, but on a road, I don't foresee any significant gaps between them.
On a track is where the LSD M Differential, poise and balance of the E46 M3 would really come into play and the M1xxi would very much struggle, especially those low/mid speed sharper corners where the M1xxi just wouldn't be able to put down it's power at all and would be left trailing.
RE: the Carwow video - there were a couple of things that played straight into the M140i/840d and very much away from the M5. Firstly, never use launch control on an M car, even on ones as modern as the F80. It's hopeless. The only reason to do it is if you want tyre smoke, noise and to look cool. It's terrible for actually giving you a good launch. And secondly, 3rd gear at 50mph in an E60 M5 is very much out of it's power band. I'm not sure where the E60 M5 makes it's power, but it's very similar in construction to the E92 M3, which makes it's full power at 8300rpm and redlines at 8400rpm. These are cars that very much have to live from 6krpm upwards to get the best from them.