Is that what that post was in reference to? None of that was mentioned aside from a general issue of taking multiple taps to open an app (which is what was replied to).
If that was it (which really should have been mentioned to begin with), then sure, that's certainly there, for a number of years now since iOS 7. Nothing really new about it now in iOS 9. It's not good, and plenty of complaints about it when iOS 7 came out, but that's the design change that was made and isn't anything new for a number of years now.
What he's talking about is how unresponsive the phone goes to any tap/swipe and even home button presses sometimes while the device is settling following an animation.
For example, when I unlock my phone, and the icons look pretty well settled, I still can't tap or swipe on anything for an extra 500-1000 ms. All those missed taps/swipes makes the phone feel really sluggish.
You're right that it's been a problem since iOS 7. 7.0 was an absolute nightmare for it, and for those 6 months, people said they "have no issues" and acted like it was nothing. When 7.1 came out and halved the delays, it became pretty evident just how slow 7.0 was.
The fact that it's been years is true, but that begs the question: why doesn't Apple have any interest in making the phone feel fast again? Why is an iPhone 5 on iOS 6 so much faster to use than a 6?
I honestly have to wonder about their priorities these days. I think they'd rather turn my Music app into an extension of the store than make the phone more pleasant to use.