Telomere length as presently measured in white blood cells is a measure of immune health before all other factors: how often are new cells turning up with long telomeres (thus how well is the thymus and bone marrow stem cell population doing), how often are existing cells dividing and shortening their telomeres while doing it (how much stress is the immune system under, how much war is it waging), how many senescent cells are hanging around lowering the average, that sort of thing.
Exercise is very well associated with better immune function. So not a surprising result beyond the fact that they actually managed to get a result at all, as telomere length measured this way is actually a pretty terrible metric of aging. The correlations with aging only show up in large populations, and even there you'll find as many failures to identify associations as successes in the literature. For an individual knowing your immune cell telomere length won't tell you a great deal that you don't already know, and nor will changes over time. The numbers will be all over the map, and won't compare usefully at all with other individuals in your circumstances, unless you have a few thousand of them to compare with.
If you want a decent biomarker that might actually prove to be actionable, DNA methylation patterns after the model pioneered by Horvath et al look fairly promising. (There's even a Florida company offering an implementation as a service these days).
The sitting question is generating a lot of ink in the research community. All sorts of large epidemiological studies have tackled the topic. I think it remains unsettled as to whether it is the sitting or whether it is the inactivity: decent arguments from data could be made either way. If pulling in data from the broader context, however, the inactivity looks more compelling. Accelerometer studies are becoming more common since the miniaturization and cost reduction that came with cell phones, and these are showing that even very low levels of exercise appear to make noticeable differences to outcomes in later life - at the level of housework and puttering around the garden.