Where's the Proof That Mindfulness Meditation Works?

That seems to be one of the exact concerns of the experts cited in the article:

"Many of the studies on mindfulness and meditation, the authors wrote, are poorly designed—compromised by inconsistent definitions of what mindfulness actually is, and often void of a control group to rule out the placebo effect."

You're right, in Theravada alone, there are 40 types of meditation, most of which could be considered a mindfulness meditation. Though it seems like when we talk modernly about 'Mindfulness Meditation' it's only referencing Anapanasati ('Mindfulness of Breathing') or Vipassana (Insight Meditation), although there have been some studies on Metta Meditation (unconditional loving-kindness).

> Similarly, you could focus on a particular subset of martial arts practices and find they are ineffective, but then mistakenly label all martial arts as ineffective.

i feel silly pointing this out, but doing any sports will always be effective. It will have at least a minor positive effect on health unless the person is ill in some way. In which case it will still be effective, albeit not in a good way