Should I connect one cable to each outlet in a two-gang box?
No. You have an upstream cable (source power) and a downstream cable (which feeds something else--more outlets or lights), and they need to be connected in order to maintain continuity throughout the circuit. 

You'll need either pigtails (best practice, but a bit messy), or jumpers connecting the two receptacles (simpler, relies on the outlet hardware more).

Your fundamental misunderstanding was that you'd have two source cables connected to one outlet. That would result in an odd (and potentially dangerous) situation. An exception would be when half of the outlet is switched, and fed from a second cable. The telltale sign would be removed tabs on the sides of the outlet.