Don’t worry, this isn’t offensive and you phrased it just fine!
Although this happens to more than just black people (I think this happens to mostly everyone), yes skin color changes all the time. A lot of the time it does get darker, while other times it gets lighter. When I was a baby my skin changed constantly going from this:
to back to this:
All during my first year and my skin still changes to this day. In the summer it gets much much darker and then lightens in the fall (even though it isn’t as dramatic as when I was younger). Like I said this happens to more than just black people and it makes sense for Clementine to get darker as she got older.
Also Clementine’s skin wasn’t the only thing Telltale changed either. In season two Bonnie’s freckles disappeared because in winter that’s what happens to most people with freckles, they fade. It’s clear that Telltale changing Clementine (and Bonnie’s) skin was them showing how Clementine has aged two years and how they are reacting to their surroundings.