I am not sure if I like this word, but at least it's better than multi-media, which used to be the hip word for what happens to media when it finds computers.
Some meanings to the word from Webster's Encyclopedic Unabridged Dictionary of the English Language:
converge, v, -verged, -verging, 1. to tend to meet in a point or line: incline towards each other, as lines that are not paralell. 2. to tend to a common result, conclusion, etc.
convergence, n, 1. an act or instance of converging. 2. a convergent state or quality. 3. the degree or point at which lines, objects, etc., converge. 4. Physiol. a coordinated turning of the eyes to bear upon a near point.
The last is perhaps the most suitable interpretation: Convergence media in the meaning of a coordinated turning of the eyes to bear upon a near point, the near point being the computer, and with all media coming together here, the attention turning to the computer and with the attention, all eyes.