It doesn't have to be game time, as the article says it could be time since level or some other trigger. It's basically about any time based counter you need for a time based effect, such as a predefined cyclical wind effect on trees or waves in water. The article also explains why it has to be precise, looping effects will behave oddly if the loop is not occurring precisely. Splitting the number into a large part and a precise part doesn't actually solve for anything, it just moves the problem into "how do I make arbitrary effects precisely loop based on the 2 parts of the time" instead of "how do I make arbitrary effects precisely loop based on the time".
It doesn't move it to 100 days, it'd move the problem to 10 minutes. Shaders can't just take a large number as a large piece and small piece unmodified, solving for this in the logic is the same as solving for the original cycle matching problem.