"Accurate to within 100 light years" isn't really a meaningful statement. The page you linked to is a simplified explanation that says the method is only accurate enough to be used for stars within 100 light-years of Earth, which is approximately true. We have measurements of more distant stars, but they become increasingly inaccurate with distance.

To be more precise, the relative error of a parallax distance measurement is proportional to both the measurement error and the distance. For example, the Hipparcos mission measured parallax with an accuract of roughly 0.001 arc-seconds. That corresponds to a 0.1% error at a distance of 1pc (~3 ly), or 1% error at a distance of 10pc, or 10% error at a distance of 100pc, and so on.

Note also that the page you linked was written sometime around 2002; since then, more sensitive measurements have been done, e.g. https://arxiv.org/abs/1401.0484v1