ShortDOI Service (2013)
shortdoi.org
shortdoi.org
Even it might exist for more than 8 years, I never see it used in the wild
Probably because the problem it tries to solve is mostly a non-problem in practice. I've hardly ever seen "very long" DOIs. In fact most I encounter on a day to day basis are so short that you could reasonably spell them out loud if you'd have to.
EDIT: Okay, it's better than I expected. It currently gives you a 4 character id (e.g. https://doi.org/f655), which is so short that e.g. one would quickly copy it from a presentation slide.