You are right that the type of power doesn't matter (AC/DC), but the voltage does NOT dictate the gauge of wire needed. It can dictate the insulation used, however most wire I have seen is rated to 600V.
The original post was probably correct - in this application - that the DC power distribution will need larger gauge wire. The AC/DC power supply normally in a computer is not terribly inefficient, so the DC power supplied to the computer will need to supply almost the same number of watts as the AC circuit. Unfortunately the DC power is supplied at a much lower voltage so the current must be raised to compensate for this.
Of course it is possible that they are distributing high-voltage DC power (maybe ~250V?) and including a DC/DC power supply in each computer. This would let them run smaller gauge wire, but increase the cost of the components in the computers. Additionally it would eat into the efficiency of the system, which would seem to be the biggest benefit of a central AC/DC conversion.
As for the trains, I would be surprised if they were running on low voltages. Copper is expensive, and thicker wire will also make a motor less efficient for a given frame size.