That’s an interesting quote & distinction between “infinite, fading time” and “finite and fading periods of time”.
Scripturally speaking it is true that God existed before He created the eons (Heb.1:2; 1 Cor.2:7). So He could be understood as infinite in time past whereas the times of the eons (times eonian, Titus 1:2; 2 Tim.1:9) are not, but had a beginning.
Some also take the position that the eonian times have an end (based on, for example, Heb.9:26; 1 Cor.10:11), which seems that it may agree with your quote. Following are some sites that elaborate on, give charts & a concordance re that viewpoint: