This is at least consistent. Let's try to think of numbers as functions. Then dots or juxtaposition must mean function composition, right? Then, f(x)=f⋅x is consistent with arithmetic as we know it and this dual interpretation of dots. I suspect that it's also the only such consistent mapping from numbers to functions, but couldn't prove this right away.
It is used particularly in things like 3(x + 5) or (a + b)(a - b).
The notation of the article logically follows because e.g. (4) = 4 but using that as a "cheat" to enable multiplication of numeric literals using adjacency is very rare I think.
Suppose we expand that first example. I would write: 3(x + 5) = 3x + 3⋅5 The notation I'm talking about writes: 3(x + 5) = 3x + 3(5)
It's that 3(5) instead of 3⋅5 I'm talking about.
I'm used to see multiplication written as 3⋅12 or sometimes 3×12, but recently I encountered this notation using parentheses, 3(12), and now I see that in this article too. Is that commonly used? It looks weird to me, and not very readable, perhaps just because I'm not used to it. To me 2⋅2⋅2⋅3⋅7 is much more readable than 2(2)(2)(3)(7) (which at first sight looks like function calls to me). Is the parentheses-notation used just to get rid of the explicit multiplication sign?
I guess there are situations where you can't easily use a proper multiplication sign, in which case I can see the parentheses notation as an effective alternative. But I've seen it used in handwritten equations too, so that can't be the only explanation.
Just wondering.