Getting a point to move along a curve is quite easy. First of all it is important that you use Realize Instances as @Chris mentioned in the comments, because from the String to Curves node's output you only get instances from which you cannot sample any position.
After realizing, you can use a Sample Curve node to get the Position anywhere on the curve(s), just by setting the Factor from 0 (start of the curve) to 1 (end of the curve). The important thing here is to check the option All Curves, since the text is composed of multiple curves/splines. With this option enabled, the factor 0 to 1 goes from the start of the first spline to the end of the last spline. Otherwise 0 to 1 would only be start and end of the spline with a given index.
With a Points node plugged into a Set Position node you can now use the Position output of the Sample Curve node to place the point at a certain position on the curve, given by the Factor. Animating the Factor moves the point along the curve.

The only problem however is the way the point moves along the curves. Fortunately it moves along the characters from the first to the last, but within each letter the direction seems a bit weird (at least in my opinion), as you can see in the animation below. I'll leave this answer to be improved by anybody who has a good idea how to change the spline's direction, so that it maybe starts at the top left or bottom left of the H instead of the right side going to the left. On the other characters it start left, maybe it is dependent on the font so I will not bother a lot about it now, the general movement along curves is there.

Oh yeah, maybe it is the the font. With a regular Arial font the movement looks less weird i.e. it starts at the bottom left of a character.
