There are mechanical fasteners, and there are fasteners. Wikipedia doesn't seem to distinguish between the two, based on the single quoted sentence in the question. Mechanical fasteners have been described at great length by other answers already (the question content provides an adequate definition of a mechanical fastener too).
The question specifically asks the following:
I figured the use of fasteners doesn't necessarily require machinery
so if it's not the definitions related to machinery then it must mean
the physical forces that you apply to the fastener when used to join
No, that is not necessarily correct. There are fasteners such as buttons, for example. Let's put that aside, as a button doesn't actually use "fastener" in its name. A much better example is a hook-and-eye fastener. Hook-and-eye fasteners do not use adhesion, mechanical forces nor machinery to create a join. See below for an illustration.