Having read half the paper, the treatment group took 600mg ibuprofen daily for 14 to 44 days to induce the reported effect of compensated hypogonadism, though the 12 and 24 hour effects on testosterone were apparently easily detectable on ex vivo testicle samples. So, maybe if you need your testosterone, keep off the OTC pain medications. And probably don't donate samples of your testicle either.
Interesting paper though.