For example, let’s say you’re playing a first-person shooter game. When zooming in with a sniper rifle and trying to precisely aim at small targets, a high DPI could be valuable by allowing you to smoothly aim with small mouse movements. When playing the game normally without a zoomed in sniper rifle, this high DPI may be too sensitive.
I just want to point out that this is not necessarily true. When you're zoomed in with a sniper, you want large mouse movements to equate to small movements on screen - IE a low DPI. That lets you keep the crosshairs on a target while they're moving, as well as make fine adjustments. A high DPI in this situation would mean your aim would be jumping all over the place. A semi-high DPI would be useful for scoped (non sniper) assault rifles where you're tracking a target closer to you.
When playing normally (which I would assume to be running around with an assault rifle), you want a medium to high DPI. That lets you quickly move from target to target as well as change direction with minimal mouse movements. With an assault rifle, accuracy isn't as important since the higher fire rate can compensate for missed shots. A higher DPI is especially important with shotguns.
TL;DR: I think the paragraph about the usage scenarios for high DPI in FPS' might be backwards, from my experience at least.