Repeating "people can't multitask" as many times as possible doesn't make it true. People can multitask. Some can do it better than others, but everyone can.
People can multitask perfectly fine when the tasks they are doing are automatic (that's why you can usually drive and have a conversation [with a passenger] at the same time without any difficulty). When you're doing multiple things that require cognitive resources, your brain has to share its (surprisingly limited) short-term computational power/memory, resulting in decreased performance.
There aren't many things people do on computers that are automatic (at least not many things I do). But I'm typing this on a computer with three monitors, and I can say objectively that my efficiency is way higher than if I had one small screen with at least two clicks to get to my next app.
However, the argument that multitasking on computers is bad because humans can’t multitask is flawed.
That was right in the article itself.
I believe the author's point is that focus/attention is more important than being able to "multi-task". Refer to Daniel Simons's experiment (the invisible gorilla) on selective attention.