The paper defines gym-based strength training as "working out at a gym/weight training/exercise biking". That is, participants in the study were merely asked if they had done one of those three things in the past four weeks, and if they had, they were considered to have done "gym-based strength training".
This is of course already flawed methodology: using an exercise bike consists of a very, very large number of repetitions of a very, very sub-maximal load. This is not gym-based strength training in any form.
Checking whether you've engaged in the activity "working out at a gym" is also a very poor indicator of having participated in consistent and effective strength work. The vast majority of individuals do stupid shit and make no progress, year-after-year.
So, I suspect the reason that the two categories confer roughly equivalent benefits is because when you perform both in an ineffective and poor manner, all you're really doing is exercising (not training), and the exact form of exercise becomes irrelevant.
If you were to do a study that was tightly controlled/regulated and consisted, say, of doing a linear progressive overload program (where you see untrained individuals gain tens of pounds of muscle and put on hundreds of pounds onto their squats) I theorize you'd see very different results. The physiology of a muscular individual who squats over 400 lbs is very different from the physiology of a skinny individual who does push-ups every morning and morbidity is rooted in physiology.
Finally, there is no bodyweight exercise in existence that can provide adequate loading of the posterior chain/lower-body. The musculature is too vast/large and doing a bunch of air squats doesn't provide adequate stress to introduce an adaptation in all but the most untrained of individuals. Adequately stressing the smaller musculature of the upper body is easier--especially at first--but even here adaptation quickly slows due to the inability to effectively load the body in a progressive manner.
So no, bro, you probably have to lift. And yes, bro, once again we see that the entire field of exercise science is basically nonsense.