For home theater I always use line level. For 2-channel music-only all analog system (no DSP/bass management), I prefer the sub via high-level outputs than line level every time.
The argument for speaker level input is that, since you want the sub to be a seamless extension of the mains, it is better to drive the sub with the exact same signal as the mains. If there is any coloration or non-linearity in the amp, the sub and mains see the same coloration and non-linearity and they sound more seamlessly integrated. The counter to that argument is that the coloration and non-linearity of the amp isn't significant enough to make difference.
The argument for line level is that there is less noise/distortion using the line-level output, which is true. The counter to that is that the added noise/distortion of any quality amp is trivial (especially compared to the high measured distortion levels of all subwoofers).
There is an argument for and against both sides. It's "mains and subs being driven by identical signals with slightly higher distortion" vs "lower distortion but with subs and mains being driven by less uniform signals".
The article is pretty senseless -- it talks about "delay" in the amp as if amp delay is the justification for speaker level, which is ridiculous, the delay of an analog amp is infinitesimal. Then it asks "why would adding the amp delay be good?". The reason it would be good is because, if there was amp delay, the subs and mains would be delayed the same amount vs the mains being delayed more than the subs. But delay is not the issue in analog (it is in DSP systems) -- coloration and non-linearity of the amp is possible, and it is better for the mains and subs to see the same thing.
The best thing to do is to listen to both -- line level vs speaker level and choose which sounds best. For 2-channel analog systems, I've always found speaker level sounds a lot better integrated with the mains than line level. Everyone should choose based upon what they hear when they try it. Most of the people who have told me unconditionally that line level is better have never tried speaker level. Some of them admit they have never tried it and refuse to try it because they know the distortion is lower. It's true that distortion is lower, but they are ignoring the uniformity of signal advantage of driving both subs and mains from exact the same signal.
I would not dream of saying which is best for anyone else, but everyone should try both and choose what sounds best to themselves.