Look at any music app, and you'll see that the pause icon does in fact have meaning absent of a neighboring play button: music apps hide the play button when music is already playing, and it's still clear how to pause. Many video players on the web show pause controls even in the absence of next/prev buttons, let alone a play button.

The context required to parse || as "pause" is just being in a context where pausing is possible. But we've accepted even less context-specific iconography for controls and navigation than even the pause icon; for example, why does × mean "close" when it's in the upper-right corner of a screen? It's fairly arbitrary, but — well, it means close, and it's not confusing. I think the hamburger icon in the upper-left corner of the screen is starting to (or already does) assume the same ubiquity: "main menu."