This difficult to estimate even in developed countries. Best I could find for East Asia, in general, is this from the ILO, from 1998 (duh!):
The sex sector in the four countries [Indonesia, Malaysia, Philippines and Thailand] is estimated to account for anywhere from 2 to 14 per cent of Gross Domestic Product (GDP), and the revenues it generates are crucial to the livelihoods and earnings potential of millions of workers beyond the prostitutes themselves.
[...] In Thailand, for example, close to US$300 million is transferred annually to rural families by women working in the sex sector in urban areas, a sum that in many cases exceeds the budgets of government-funded development programmes. For the 1993-95 period, the estimate was that prostitution yielded an annual income of between US$22.5 and 27 billion.
The GDP of Thailand was about $200 billion back then (in 2015 dollars), so 10% doesn't seem outlandish. In fact it was probably more, percentage wise, in 1995 dollars.
Another press article, also from 1999 says
A study by a Thai university estimated the sex sector at around $25 billion, or 12% of the country's gross domestic product.
There are no other [relevant] details, but I suspect it's referring to the same dataset.
In 2015 Havocscope said that about US$6.4 billion in annual revenue was being generated by the trade, a figure which accounted for 10 percent of Thailand's GDP. Havocscope says that sex workers in Thailand send an annual average of US$300 million to family members who reside in more rural areas of Thailand.
So I suspect that's where the newer claims come from. The original article cited by Wikipedia doesn't load for me. And given that it's dropping the same US$300 figure as the much older ones, I suspect the actual data is the same, and probably just extrapolated i.e. carried forward.