When the tower was constructed in 1887, multiplexing technology was probably not available (I'm not so sure of the timeline in Europe). By 1913 it likely would have come into use. However, multiplexing really isn't a factor here, as the tower seems to have been built to serve local loops. Since these loops go to subscriber telephone sets, there's no option for multiplexing without expensive and maintenance-intensive equipment at customer premises. Multiplexing of local loops is called "pair gain" and wouldn't be developed until later, and it was never really that popular in most phone systems. Outside of suburban areas, it's typical that each copper pair runs directly to the exchange. Historically, and today, there is rarely any active equipment (or since the 1950s or so even passive conditioning) on local loops, they're just wires from the exchange to the phone.

As for why you didn't see similar constructions in other cities, this was definitely an unusually large telephone office for the time. In the US, a city exchange of the late 20th century would usually have just hundreds of lines, many of them multi-party. Telephone companies scaled up by building more exchanges, rather than a single very large one. When they got into these kinds of subscriber numbers at an exchange, the F1/F2 cable scheme was in use to avoid this kind of wiring. It does seem to be the case that telephone adoption was unusually rapid in Sweden, I find one (poorly sourced) claim that there were some 4,800 telephone subscribers in Stockholm in 1886 which would very likely make it the most telephone-rich city in the world. The situation of the tower seems to have developed in part because its builder, Allmänna, was consolidating the Stockholm telephone market through acquisitions and made a decision to centralize the many acquired customers onto on exchange.

What I'm a little confused about here is the lack of cables. The other big reason you didn't see constructions like this in the US, even in places like New York City, is because subscriber loops were quickly moved into lead-sheathed, paper-insulated multi-pair cables. These could contain hundreds of pairs. Cables were pretty much reaching maturity when this tower was built. I am curious as to the reason that multi-pair cables were not adopted more quickly in Stockholm, but it may be as simple as the considerable investment in this tower making open wire the preferred option for its short lifespan. In any case, the common claim that underground cables obsoleted the tower rings hollow to me, or at least misses an important detail, as aboveground cables were already in use in the 1880s. I suspect that modernization to cables was just deferred in Stockholm until it happened to also make sense to move to duct or pipe systems. In the US, it was more common that telephone exchanges switched to overhead (aerial) cable to manage exactly the wire sprawl issue that this tower exemplifies, and then only later (if ever) started to bury cables.

This article has more photos of the tower, but unfortunately not much more technical history: https://rarehistoricalphotos.com/the-stockholm-telephone-tow...

And this includes some photos of other parts of the Stockholm telephone network. The tower was not the only impressive construction required to manage this many open-wire pairs: https://thehistoryinsider.com/when-the-sky-over-stockholm-wa...