Why are Aamir Khan's movies so popular in China?

It just started with 3 Idiots' success in China's pirated market that made it into their top 12 list. And then they just captured the opportunity and released all of Aamir's later films in China which also made success due to relatability with Chinese audiences.

Forbes covered it quite well:

There was really no way to make money in China’s home video market because virtually every foreign film went straight to pirate DVD distribution, with no opportunity to earn Chinese receipts via theatrical release.

But oddly enough, the pirate market was precisely where Aamir Khan first gained a foothold with Chinese audiences. The 3 Idiots story, which follows the lives of three fellow college engineering students through the trials and tribulations of university life and the years thereafter, explored issues and topics that also happened to be directly relevant in China. The story’s themes of friendship, academic challenge, and nostalgia resonated beautifully with young Chinese viewers, who saw themselves and their lives reflected in the Indian characters. Aamir Khan’s character Rancho was particularly appealing to the Chinese for his eccentricity and his bold approach to challenging authority and living life according to his own rules. 3 Idiots became a cult hit and is to this day China’s 12th favorite film of all time as measured by ratings on the film review site Douban.com.

They even released it later in China with good success. And this even opened the gate for Khan in China's market.

Continuing from the same article:

Most importantly for Khan, 3 Idiots ignited a fanbase that has grown exponentially since 2009. By 2013, when China's theatrical market had exploded to become the world's second largest, the audience was ready to pay to see Khan's movies on the big screen.

His hit action-thriller Dhoom 3 received a 2,000 screen release in 2014 in the PRC, the largest ever for an Indian film, and it grossed $3.8 million, a staggering total for the time. The next year his satirical science-fiction comedy PK opened on 4,600 screens and completely upended expectations, earning nearly $20 million in China, more than any Indian film had ever earned anywhere outside of India.

And Dangal even became India's highest grossing film ever till now due to China's collections only beating Baahubali 2.

This success is also covered in The Diplomat, which highlights that his films adress issues Chinese society tends to struggle with, too:

Referred to as “India’s conscience,” Khan’s personal story has been widely reported by Chinese media. His most inspiring point is that he has made great efforts to confront various social issues in Indian society, such as poverty, education, sexual abuse, gender inequality, and discrimination. (All these issues are relevant to China’s society, too.) Not only did he present these problems in his movies, he also created and hosted a television talk show, Satyamev Jayate, targeting these sensitive issues directly in real life. This talk show has been translated and broadcasted by a Chinese website.

This viewpoint is extended to Indian films in general in this Times of India article:

Professor Gupta explains why Indian movies are resonating in China, “Their and our social issues are the same - gender discrimination, poverty, lack of quality education. They are dealing with the problem of girl education, patriarchy and parents struggling to find a good school since nursery education, the way it is shown in Dangal and Hindi Medium. Chinese students, even though struggling with spoken English, enthusiastically participated in the classroom activities, and were curious to know more about India and its cinema.”

Even covered in this YouTube video too (with Professor Arun Gupta's audio interview):

Which covers lots of similar aspects.