Switched Mode PSU ?
Of course, it is difficult to do 100A in a linear PS without frying eggs.

Ok, let me try:

There is a 4 bit weighing of each colour (this is for Steve, thus the 'u' in color) this constitutes not intensity but "weight". in other words, if the "weight" is 3 (0011) the particular colour will get 3/16 of the intensity.

Each LED is controlled by a constant current generator with an I matching full intensity.

So, to achieve a colour the 3 colors are loaded with the corresponding "weight" (e.g. 0 blue, 7 green and 8 red for yellow or 0 blue, 0 green, 15 red for red).

one method would be to run 16 pulses on a separate pin (all chips in parallel) this way

pulse# weight weight weight weight
(binary)  8      4      2     1
0000     off    off    off    off
0001     off    off    off    on
0010     off    off    on     off
0011     off    off    on     off
0100     off    on     off    off
0101     off    on     off    off
0110     off    on     off    off
0111     off    on     off    off
1000     on     off    off    off
1001     on     off    off    off
1010     on     off    off    off
1011     on     off    off    off
1100     on     off    off    off
1101     on     off    off    off
1110     on     off    off    off
1111     on     off    off    off

The "0000 nothing on" is not a mistake, it is the time in which ambient light is measured.
One method
The overall intensity would be controlled by e.g sending 16 pulses every 8 milliseconds, if it took 8ms to send the pulses there would be full intensity of the entire sign, if it took 4ms the intensity of the entire sign would be half.

This is one possible way to do it, others may be used.

Erik