Math is not just a part of physics. Heck, even applied math is not just a part of physics. And even in physics, I learned that there are two types of mathematical thinkers: geometers and algebraists. It would be a mistake to assume that all math that is part of physics is geometry, like this author does. General relativity is most intuitively geometry, and quantum mechanics is intuitively algebra, though you can formulate both the other way. For both math and physics, I think you need both even though most of us tend toward one or the other.
For example: the determinant of a matrix only fully makes sense if you understand it as both the change in volume of a paralellipiped, and as the product of the eigenvalues. These are the same mathematical statement, but one of them leads to a more geometrical way of thinking and the other more algebraic. Even if you are more of a native "algebraist" like me, remembering the geometric definition of the determinant can still help.
It may be that French math schools have all taken crazy pills and kicked the geometers out. The author is obviously more geometrically inclined and therefore rather irked about the whole thing. Though he might be right: if he is considering Landau and Lifshitz to be "not abstract" maybe they are starving for more grounded math education in France.