Your definition strikes me as accurate: to force, press, squeeze into an insufficient space. The thing being forced in has to get smaller or adjust in some way in the process of being forced in or it won't fit. Cramming a suitcase full of clothes, for instance, means the clothes become compressed (though, arguably, the suitcase may also expand... I don't think that's the "cramming" part, and certainly not by the definition you've provided).
The first instance of "cram" used in this way in a Google News search at the moment (as opposed to "students cram for their exams," which is a different though related usage) is "designers cram entire hotel room into a suitcase." The concept implies that there is not (or doesn't appear to be) enough space in the suitcase.
If I "cram" my socks into my sock drawer, the drawer doesn't expand, the socks contract.
Part of the issue with the cramming of one's mouth with a liquid--at least for me--is I'm having trouble visualizing it. Cramming your mouth with food is easy, but liquid consumption works differently than food consumption does. You can "gulp," "guzzle," "swig," or more colloquially "knock back" or "pound" especially alcohol, but none of these verbs implies the overfilling of one's mouth, rather they imply only rapid consumption. They certainly don't imply anything akin to the definition of "cram."