Strangely, shorter telomeres is not actually a new idea here AFAIK.

Just because a mainstream news article says that something is a new method doesn't mean it is. If you use the word "strangely" when reading a mainstream media article about science it's a good heuristic to instead go to the actual study.

In this case http://www.sciencedirect.com/science/article/pii/S2352396415001024 (open-access)

I would also be interested in a very rough guess of whether this may be an expensive or cheap test.

Rather cheap. They describe their method:

BTL was measured using quantitative real-time polymerase chain reaction (qPCR) (Cawthon, 2002). Relative BTL was measured by the ratio of the telomere (T) repeat copy number to single-copy gene (S) copy number (T:S ratio) in a given sample and reported as relative units expressing the ratio between test DNA BTL and reference pooled DNA BTL. [...]

Taking blood samples and running PCR are both not complicated things.

A bit googling around finds 400$ as a retail price (http://www.repeatdx.com/products/pricing-and-cpt-codes/) for telomere testing. There seems to be a failed Indigogo campaign that used 99$ as the default price but was target at salvia instead of blood.