Typing for 8 hours a day places the muscles and tendons under much more stress than any strength training or stretching routine a physiotherapist might prescribe to someone suffering from RSI.
And yet 20 minutes of light arm exercises (lifting weights from the wrists, hanging from a pullup bar etc) 3 times a week can make one much more resilient to the effects of RSI, even though it's much less volume than typing for 8 hours each day.
What am I missing here?
The "repetitive" part.
Repetitive motions can be interpreted by the body as an injury, which in turn can lead to inflammation, which can increase muscle tension, which can decrease elasticity, and so on.
Stretching/strengthening the related muscles can help reduce that inflammation by increasing the range of motion, correcting imbalances, increasing capillarity and the ability to withstand repetitive use.
That said:
Typing for 8 hours a day places the muscles and tendons under much more stress than any strength training or stretching routine a physiotherapist might prescribe to someone suffering from RSI.
"Stress" here is being used in two different ways. One is volume stress, one is load stress. They're not the same thing, and the body reacts to them in different ways.
