There does not appear to be much evidence of anything on the scale of what happened in the Americas but there were some significant population decreases caused by diseases introduced by non-Europeans in the Old World. The best evidence we have is from Japan. Whether all of these were introduced into virgin populations is uncertain but it does seem very likely in some cases at least.
For Southeast Asia (at least), a possible key reason for the apparent lesser severity of epidemics is that
access and use of large domesticated animals prior to European arrival
may have given Southeast Asian populations more resistance against
pandemic diseases, especially compared to the catastrophic mortality
witnessed in the Neotropics.
Source: Noel Amano et al, 'Archaeological and historical insights into the ecological impacts of pre-colonial and colonial introductions into the Philippine Archipelago'. in The Holocene, Volume: 31 issue: 2 (2021)
However, in our search for evidence, we are hampered by the paucity of sources for periods before European contact:
Knowledge of disease in the Southeast Asian past is severely
constrained by some of the same features that give the region its
uniqueness. Human remains, and written records of disease, deteriorate
rapidly in the acid soils, heat, and humidity that are characteristic
of this part of the world.
Source: Kenneth F. Kiple (ed.), 'The Cambridge World History of Human Disease' (1993)
You cite the example of a small pox outbreak in Japan in 735 – 737 AD, but there may have been smallpox epidemics there dating back to 585. The epidemic of 585-587 is believed to have come from Korea, and there was an epidemic in 552 which was probably either plague or measles. Both these epidemics were blamed by adherents of the Shinto religion on the recent introduction of Buddhism from Korea. The Buddhists, in turn, said the 585 epidemic was retribution for the destruction of Buddhists temples and monuments. Although there are no specifics on casualties,
Thousands of people were afflicted with the disease [smallpox], their bodies
covered with sores, and many died. Even the emperor and the chief of
the clan leaders were infected....autumn of 585, the emperor ordered that the Buddhist temples be rebuilt but banned conversions. He died shortly thereafter, becoming perhaps Japanese royalty’s first smallpox victim. He was succeeded by his brother Yomei... He too was stricken by smallpox in 585 and died in the continuing epidemic two years later.
Source: George C. Kohn (ed.), 'Encyclopedia of Plague and Pestilence: From Ancient Times to the Present' (2001)
In 994-5, there was what appears to have been an even more serious epidemic in Japan. The origin of this epidemic seems to be unknown but the severity of it suggests that it was affecting a virgin population:
Historical sources are agreed on the severity of this epidemic, which apparently killed many in the elite ruling class over a brief
two-to-three-month period.... Overall, it is estimated that more than half of Japan’s population died during this epidemic
Source: Kohn (ed.)
Then, in 998 and 1025, Japan was hit by measles epidemics which, according to a local chronicle, infected everyone (all ages and social classes). The origin of these epidemics is not stated, though, but China or Korea seem the most likely points of origin.
In 1867, a malaria epidemic killed 31,920 people. It had been introduced in 1866 either by Indian or African labourers (but possibly by British soldiers). The final death toll was around 43,000 out of a population of 330,000. This Mauritian Ministry of Health document states:
This was the worst calamity that Mauritius has known and it had serious economic impact on the island. Many people moved from the capital Port Louis (a coastal town at that time) to the high plateau (Curepipe) in order to escape the disease. During the next 100 years malaria became endemic and caused recurrent epidemic with high mortality – malaria was the principal
cause of death in the post world war II period.
Mortality rates for the Philippines are hard to come by. Linda A. Newson, in Conquest and Pestilence in the Early Spanish Philippines goes into some detail on the situation in the Philippines. In this book,
Newson argues that the sparse population of the islands meant that Old
World diseases could not become endemic in pre-Spanish times.
Unlike in the Neotropics, there were no big cities and relatively few
urban centres that would have hastened the spread of diseases.
Source: Amano et al
According to Newson, China had extensive trade links with the Philippines but low population density, the time it took to travel from island to island, and ‘the Filipino habit of frequent washing’ seem to have ‘discouraged the spread of some infections’ in the pre-colonial (Spanish) era. Leprosy almost certainly came from China but, although leprosy and yaws were common in the Philippines prior to the arrival of the Spanish, they were rarely fatal. In short, the circumstantial evidence suggests that fatal diseases did not become endemic in the Philippines prior to the arrival of the Spanish. However, this does not preclude local outbreaks with high mortality rates. The first recorded major epidemic seems to be the smallpox epidemic of 1591, but this came via a Spanish ship from Mexico. A Jesuit priest of the time described it as 'vicious' with one third of the population in Batangas bedridden.