TLDR: no you are not shortening your lifespan by exercising
Humans have linear chromosomes, meaning our DNA in each chromosome is a long string with 2 ends. When DNA is copied an RNA primer is added at the beginning to start copying but then removed at the end so the DNA gets shorter each time a cell divides ([Diagram](https://cdn.kastatic.org/ka-perseus-images/543664d6b0d7dde9627d6dc342d209291cf71133.png)). To combat this the ends of our chromosomes have regions called [telomeres](https://en.m.wikipedia.org/wiki/Telomere) which are essentially expendable DNA so we don’t loose anything important.
Telomere shortening is one of the [hallmarks of aging](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3836174/#abstract-1title), however it is most likely not the primary cause of aging. And there is an enzyme called telomerase active in some cells that can repair the telomeres. There is a large body of evidence showing exercise can reduce many of the hallmarks of aging and when you exercise any decrease in telomere length is either negligible (for a variety of reasons) or counteracted by stem cells/progenitor cells with active telomerase.
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