I read that part of the license agreement as a recommendation rather than a requirement (note the word "should" rather than "must"). Sometimes Mathematica is cited in research papers sometimes it is not. It makes the most sense to cite it if it was substantially used in deriving results. And the main reason from the point of view of research that I can think of for doing that is so that others who are trying to reproduce the results can do so using the original tool, or use a different tool to compare and determine whether any bugs were responsible for unusual results.

What David Reiss wrote is quite on target. In addition, you might want to cite or at least mention the software used in situations where others might be interested to know that information. But it is by no means required by the license, it is simply a courtesy to readers in situations where you have reason to believe they might wish to know that.

The internet forums may have their own requirements beyond the usual academic/authoring ones David noted, and what I note above might or might not also apply to those.

Thank You guys very much!