There is counting. Recognizing quantities (by sight or by touch). Arithmetic (+, -, *, / ). Recognizing shapes. Finding unknowns. Mapping concrete items to abstract concepts (A A A = 3 As). Using variables. Algebra, Geometry, etc, etc. These are different skills. I am sure we have all met children who can tell you that "6+9=15" but if you asked them "if mommy gives you 6 cookies and daddy gives you 9, how my do you have?" would be stumped.
It sounds from the article that they dd not eliminate all maths, just abstract symbol manipulation, like "3+4=7".
It is pretty well established by people like Piaget that there are certain windows in childhood. During those times, the mind can easily absorb certain concepts that before or after those times they either cannot or all or can only with great dificulty or other exceptional circumstances.
The most widely accepted window is the window for early language learning, where beyond a certain age you will likely never be truly multi-lingual - you will always have a first language and zero or more secondary ones. However, there are several others. Mother-bonding happens within days of birth. Arithmetic sense (the ability to count, recognize quantities and relations) is one of those that is also quite young - 4-6 or something if I recall. There is a similar window for social behavior. There is also evidence that topology is such a window.
Ironically, despite the western obsession with early reading, there is no evidence that there is any window for reading. People who learn to read later in life - even 40's and beyond - can learn to read with little trouble and quickly become indistinguishable from early readers in terms of reading speed and comprehension. In fact, there is no evidence at all that early reading has any positive effect.
There are already schools that emphasize non-academic ways of learning. For example, in the Waldorf schools, children are not exposed to ANY academics at all - not even letter shapes or counting - until they are 7. Then the academic load builds slowly up, with more emphasis on outdoor play, spoken language and song, and craft-making than on book learning or lecturing. Despite this, most of these students have standard tests as high or higher than students from other private school that place more emphasis on academics.
My personal opinion (as someone with lots of kids in school) is that our current education system puts too much stuff in kids heads that they cannot process because it is not relevant to their daily experience. It is better for kids - especially young kids, under 10 or so - to play outside, engage in imaginative play, and to develop deep emotional connections with people around them than to learn to read or memorize multiplication tables. Academics can come later.
Real Programmers don't write in FORTRAN. FORTRAN is for pipe stress freaks and crystallography weenies. FORTRAN is for wimp engineers who wear white socks.