Here are the horizons it computed from the author's location, annotated by myself to align them with the pictures from the blog post: https://imgur.com/a/AlGiDi4 (open that on desktop—imgur serves low-resolution images to mobile browsers)...and unfortunately, what the author believes to be Ireland is actually Anglesey. What he believes to be Anglesey is actually Great Orme. What he believes to be Great Orme is actually Little Orme. Essentially all the peaks he identified are in reality shifted by 1 peak to the north. And the outline of the peaks in his pictures match the outlines of the simulated horizon so there is no doubt: he saw Anglesey (70 miles) and not Ireland (~150 miles).
Here are the parameters I used to generate the first rendering (after filling them in, click "Panorama anzeigen"—direct link: https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=ne... ):
Breite (°): 53.63638 Länge (°): -2.53707 (these are the GPS coordinates that correspond to the layby where the author parked and made his binocular observations)
Blickrichtung (°): 248 (azimuth, or direction of observation)
Blickfeld (°): 7 (field of view)
Zoomfaktor: 10 (zoom)
And for the second rendering, just change these params (direct link: https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=ne... ):
Blickrichtung (°): 251.5
Blickfeld (°): 3
Zoomfaktor: 30
When I was a teenager I realized one morning I could see what could be Mont Blanc from my town, but very rarely only on specific mornings when the sun would rise right behind it. But I could never confirm because I saw it of my own eyes, without binoculars, and the right meteorological conditions only reoccured twice in my lifetime to see it. About 20 years later, when I found the udeuschle.de panorama site, I checked and was absolutely delighted when the site confirmed the shape of the peak that I remember so well matched exactly the generated horizon :-) It was at a distance of 130 miles...
EDIT: in order to see Ireland from the blog post author's location, you have to raise the camera at an altitude of about 1400m above ground (set the altitude in the Kamerahöhe field): https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=ne... (screenshot: https://imgur.com/a/AT0BAnm ) The Irish peak visible is mount Kippure, next to the red mark "Max Dist" which is 159 miles away). It's a site made for desktop browsers. You can hover the mouse pointer over any peak label and it will show the distance to it. If you click it, Google Maps opens to the given peak, etc. A really neat way to explore the Earth. By the way in the above rendering at altitude 1400m you can still recognize Little Orme and Great Orme (at about one third from the image from left). The high-altitude perspective gives an idea of how much farther Ireland is behind these peaks.
EDIT 2: at only about 900m above ground, the author could see Slieve Donard 143 miles away in Ireland (well, Northern Ireland, not the Republic of Ireland): https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=ne...