word order - Correct usage of "The" within this sentence

I disagree that "all products" implies all products in existence, because it is clear from the context that it refers only to products on this particular website.

Consider a menu that says "All prices include 10% service & 15% VAT" - one does not assume that this means all prices in existence, just those on this menu. (Not to mention that "All the products" and "All products" can both mean "All [the] products in existence").

As the definite article is used to distinguish a particular from a general, "the" in this context can be distracting. I almost expect the sentence to continue: "All the products we sell online (as opposed to those other ones that we only sell in-store)" or "All the products on page 1 (as opposed to those on the other pages)".

If you do wish to make a distinction, consider "All our products" or "All products on this website".

The choice of phrasing here is, however, a matter of stylistic preference. Any of the abovementioned examples will almost certainly be understood the same way.