Why do scammers frequently call their products a "system"?

Marketing, sales and all persuasive measures often borrow terms from science and other well respected fields, say business, to show their claims in the best light. Doing so prevents or puts off more careful analysis. Con artists, being most desperate of these salesmen, use the best analytical verbiage they can manage.

A System has the benefit of being made up of many parts. So if one part is suspect it can be claimed to be corrected by some part as yet unspecified. It's very complicated you see.

Remember, for each word you hear that alerts you to the lie fifty other people are ready to buy it because of that same word. Education is slow and people are many.

they always call these bottles "systems"

They aren't calling the bottles a "system". Using the bottle is (or part of) their system. The suggestion is that it's not just grabbing some random product from the grocery store. Someone has figured out a specific plan that involves taking some substance (or substances) in a particular dosage and frequency.

Anything that consists of several interconnected parts that together perform some function can be called a system, and almost every product does consist of several interconnected parts that together perform (or are claimed to perform) some function. Thus, practically anything that is likely to be offered for sale can, so far as semantics is concerned, be called a system; it is not false to call it a system.

On the other hand, so far as pragmatics is concerned, the word system is usually used only when a thing's being a system is somehow noteworthy; it is thus typically used only for relatively complex, ingeniously structured systems. Using that word for something relatively simple is therefore misleading, even though it is not false.

It is not false (although it is misleading) to say that a liquid preparation of vitamins is a system, because it does consist of several ingredients that work together. Alternatively, it can be argued (as has been done by Accumulation) that the regimen of using the preparation is a system.

Advertisers often try to find ways to say things that will mislead the intended audience, without being, strictly speaking, false, so it is not surprising that they make use of the word system to create the impression that their products are more complex than they are, while avoiding the legal troubles that could result from saying something that is outright false.