I'll admit I didn't read hardly any of that study, but I caught the bit about the subjects already being on anti-depressants. I'd wager the effects of exercise on positive modd would be decreased on subjects who already have a chemical imbalance causing depression.
There could still be improvements in mood that wouldn't be severe enough to stop the use of antideperssants. Or maybe it's a perceptual thing, if you're already depressed, you may have a harder time perceiving an improved mood as significant enough to report.
My own experience tells me that exercise definitely improves mood. It's common sense that the endorphines released during exercise improve mood. Exercise also improves confidence and self-esteem.
The study also mentioned that subjects who started exercise were more likely to continue doing so after the trial period. Why is this? Mere habit? How does someone who is depressed find the willpower and perseverance to continue a workout regimine if it's not doing anything for their mood?
In any case, walking is better than nothing, it should maintain a baseline level of cv fitness, but you'll never run a marathon from walking. It all depends on what your goals are.
My current project:
https://diceus.com/how-to-know-what-is-crm-software/