I can think of another possibility, which is that in order to compare a 1080p display and a 4k display properly, you need to ensure that both displays are reasonably calibrated for quality. TVs out of the box are tuned in a mode I think of as "claw your eyes out" mode, with horrid preprocessing and sharpening and all kinds of other things designed to make the TV pop out in the display room, with no regard what it does to the underlying video signal or your eyes over time. Two displays in different resolutions, both left in this mode, may look roughly equally crappy when you're sitting at home feeding it a normal video signal, rather than a crafted demo. The article alludes to this when it mentions turning down the sharpening, but typically the "mode" the TV ships in initially will do other things too, like pop the saturation up and such.
The first thing you'll want to do with a new TV is to take it out of that mode. The "correct" mode depends on the TV and some internet searching can help you out, but putting it in the cinema/movie mode is at least a first good guess.
Finally, of course, you need to feed the 4K monitor a good 4K signal, or the 4K monitor isn't going to look any better. And as the article mentions, that's sometimes easier said than done, because HDMI can't always handle it.
If after all that, you can't tell the difference at all between 4K and 1080P at point blank range on a monitor setup like that, you may have eye issues, yes, absolutely. And you may still find that you don't much care about 4K. I've got 4K on my laptop, which is nice in a couple of ways, but in general I'm really rather "meh" on it for development work. I've got two 1080P monitors at work and prefer that to a 4K setup. But I also don't care about pixelization very much compared to a lot of people, and never have. I used to read books on my 160x160 monochrome Palm Pilot, and I guess everything looks good after spending my formative years on a Commodore 64 with a 1980s vintage television. But I do at least see the difference and can easily understand why others have other opinions.