Haversine's answer makes some good points, but the problem is broader than just a "slowing down" historically. The real issue is that the correspondence between the Italian tempo terms (which originated as stylistic terms too for performance and interpretation, not just tempo) and the metronome markings has always been inexact. Metronome manufacturers created these arbitrary scales themselves, and different manufacturers prescribed different ranges for these Italian terms.
Just for some datapoints, take a look at this article, which discusses actual tempo measurements as recorded by a musician in the year 1800 using a pendulum device (before the metronome was invented). He was literally recording, for example, the tempo of how some of Haydn's pieces were performed within Haydn's lifetime.
Anyhow, the appendices in that article give a sense of how wide-ranging the interpretation of Italian markings was back then. Different pieces marked with the same tempo marking were apparently performed with tempos that could vary by a factor of two or more. Appendix 1 offers different pieces with recorded tempos that fell into these wide ranges. (I just give a selection to accord with the tempos discussed in the question.)
Using eighth note as beat:
- Largo - 60-119 bpm
- Larghetto - 95-153 bpm
- Adagio - 64-125 bpm
- Andante - 72-153 bpm
- Lento - 69-153 bpm
- Andante - 72-153 bpm
Using quarter note as beat:
- Allegro - 91-153 bpm
- Vivace - 88-168 bpm
Using half note (or dotted quarter) as beat:
- Presto - 82-108 bpm
- Prestissimo - 77-168 bpm
Granted, these tempos were recorded by one musician estimating how certain pieces were performed, but they give insight into the arbitrary attempts to try to shoehorn Italian markings into metronome ranges. Obviously things like time signature, beat groupings, and rhythmic "feel" of a piece frequently will mean that a piece with a particular Italian marking might be outside of the range any standard metronome prescribes.
The takeaway here is that while there was a general sense that certain Italian markings were relatively "slow" and others relatively "fast," there was a huge range for most of them and significant overlap, rather than the nice delineated scale most metronomes present, dividing each marking up into tidy numerical ranges.
I cited that particular article for another reason: it also produces in its Figure 1 (pp. 38-39) a scale from a "Modern Metronome," cited to have been manufactured around 1975 by Seth Thomas, which corresponds pretty much exactly to the scale in the image cited in the question. Indeed, while I'm not sure of the manufacturer of the historical metronome discussed in the question, the scale is the same one used by the French manufacturer Paquet and the American manufacturer Seth Thomas (which imitated Paquet in its "Maelzel Metronome" models).
Note that Seth Thomas was producing metronomes with this scale into the 1980s (here's an example of an electronic Seth Thomas metronome with this scale currently on sale on eBay), so we can't be sure the metronome discussed in the question was from Beethoven's time. It's likely a bit later (late 19th or early 20th century), when this scale was somewhat standard on Paquet and Seth Thomas models.
The Seth Thomas scale was notably faster in its tempo markings than the Wittmer metronome scale, which came to dominate metronomes in the past generation or two after many other metronome makers left the market. The Wittmer metronome scale is probably what most people today think of when they see Italian markings on a metronome, which is why I assume the question thinks the linked metronome's markings seem "too fast." It seems the Wittmer scale (or something close to it) is often assumed in many apps and electronic metronomes today.
Anyhow, my broader point is that these supposed conversions are really nothing of the sort, just approximations created by metronome manufacturers, probably based on no standards or research. Also, it's not clear that all metronome scales were meant to apply to the same note value: for example, the Seth Thomas scale might make more sense when sometimes applied to shorter note values, but obviously that wouldn't necessarily apply to all tempos.
As seen in the article cited above with its data from 1800, Italian markings had great overlap in their actual performance tempo ranges, so the metronome manufacturers had to create artificial ranges and distinctions among them. Although I've never really looked at this in depth, I'd guess that by the late 1800s, composers began to correlate their tempo markings on newly written pieces to the (originally somewhat arbitrary) scales of the metronomes with their imprecise adherence to Italian marking norms. But when one examines actual evidence from composers and performers who noted bpm markings in the late 1700s and early 1800s, these numbers were all over the map.
Bottom line is that the bpm range = Italian marking concept was essentially invented by metronome makers and was never very precise. The reason this metronome seems "fast" is because it was likely made by a different manufacturer than the ones commonly produced today, not necessarily because it's significantly older. (Wittmer's metronome scale dates, I believe, to the late 1800s when it began manufacturing them, roughly the same time Seth Thomas starting making metronomes. So it's not like one scale is really "older" than the other in a substantial way.)