Are there any influences of sinification in modern times?

A couple of data points:

Firstly, The Song Dynasty (960-1279) pioneered many methods of modern finance, trade, and economics. Subsequent to the Song, the Mongols ruled China and much of Eurasia. In administering their civilized territories, the Mongols used administration and economic management techniques that they learned from the Song. Indeed, they employed Chinese engineers and bureaucrats throughout their empire. The merchant classes from South Asia, the Middle East, and Europe grew greatly as a result of this style of management, and commercial activities (banking, corporate arrangements, trade management) grew as a result.

Likewise, Chinese manufactures like Tea, pottery, silk, etc, along with spices, spread to the Middle East and Europe. The royalty and the wealthy in these areas developed a taste for these goods, and empowered merchants to increase trade. (this led directly to colonialism)

Secondly, Matteo Ricci spent about 3 decades (1582-1610) as an advisor to the Ming emperors. There is much emphasis in history about his influence in the Ming courts concerning his introduction of European culture there, and his conversion of many Chinese to Christianity. Much less spoken about are the result of his reporting, and the reporting of others who followed his footsteps, about the structure of the Chinese state, especially how it was centralized, and its meritocratic bureaucracy & civil service exams, and its "strict" legalism.

Modern European states in the late 1700s and 1800s structured their post-feudal, centralizing states in a manner patterned after Chinese methods.

What does this mean?

Much of modern society, with centralized secular governments ruling with somewhat meritocratic methods, with high priorities on trade and living standard, are the result of worldwide Chinese influence over the last 1,000 years.

In summary, the whole world is currently undergoing "sinification" at this very moment, and you didn't even notice!

A side note: I've had difficulty building a non-racist definition of "sinification" as China is a really diverse place. People of the Han ethnicity in South China and North China are as different as Scandinavia and Egypt; does this mean China hasn't been sinified yet? Or does it mean the only commonality is a secular centralized state with managed economic organization ? It might be easier to discard the concept of sinification all together, and view the world as a place where ideas flow in every direction at once.

The place that springs to mind is Singapore. While physically being an island on the southern tip of the Malay peninsula, all but about a quarter of the population is ethnically Chinese.

This majority wasn't achieved until the mid 1800's, likely owing to the same factors that caused an influx of Chinese into the USA at around the same time.

There are several examples I can think of, but I admit they are all of a very mild sinification.

1. 19th Century California - There was a large influx of Chinese immigrants, whose culture has permeated into the American. The several large China-town districts in San Francisco and other towns (even New York) are a good indicator, as well as the prevalence and popularity of Chinese food in mainstream American culture.
2. 21st Century eastern Africa - There are several nations in eastern Africa currently involved in serious trade with China, mostly around raw materials supply, such as mining. This is being done mostly by Chinese companies, bringing their own personnel. Naturally, the culture is slowly being influenced by all the people visiting, though of course it's too soon to tell how deep the sinification will be.
3. Malaysia - There has been a huge Chinese influence in Malaysia over the last century or so. So much so, that it has (among other things) lead to the creation of Singapore, as the Malaysian federation tried to evade that influence.

That's all I can come up with in the time available, I'll edit the answer if anything more comes to mind.