Absolutely. Imperial China had an extremely interesting (imo) aristocratic class which provided the backbone of the empire's ruling, civil elite from the Song dynasty all the way through to the end of the imperial system in the early 20th century. The men and their families who comprised this class of people were the 士大夫, variously known as the scholar-officials, scholar-gentry, or the literati class. As the English names might give away, this aristocratic class was not strictly based upon hereditary privilege or historical familial wealth but rather was established upon the education and cultural attainment of its members. The relative esteem of China's gentry class stems from elite Chinese society's long history of reverence for the teachings of orthodoxy Confucianism. Very simply, the Confucian world order broadly delineates society into broad categories. In descending order of prestige, they are: the scholars, the farmers, the artisans, the merchants, and the mean people. So scholars have been (and continue to be) widely esteemed throughout history and the mid-late empires (10th century - 20th century CE) almost exclusively recruited from this scholarly class for appointment into the civil administration necessary to maintain the functions of government in China's empire.

The 'marker' of an individual who was a part of this upper class was usually the successful attainment of an educational degree. In the Ming dynasty, degrees were stratified into three (technically four) levels. At the bottom was the 生员 (shengyuan) at the county level, usually undertaken by children at or around the age of adolescence. Above it was the 举人 (juren) at the provincial level and finally the 进士 (jinshi) at the palatial level. There was a level below the jinshi, the national exam, but advancement from the national exam to the jinshi was automatic and all individuals who passed at the national level would become a jinshi with only the final grades determining the level of 'seniority' any one individual jinshi holder had within his class. The shengyuan was not particularly difficult to attain as evidenced by the relatively large number of individuals in Chinese history who acquired one but there were very, very high attrition rates from the shengyuan to the jinshi. This was by design and necessity as the ultimate goal of these exams was to screen people for literacy in the Confucian Classics and for fitness in government roles. Since the imperial bureaucracy was relatively small compared to the total population of test takers, high levels of failure were a natural end result. Nonetheless, people who stagnated at even the very lowest level of the examination system were accorded some degree of prestige and respect as technical members of the scholarly (read: aristocratic) class. However, I must emphasize that aristocratic did not necessarily correlate to personal wealth. There is a whole other can of worms when it comes to the economics and social aesthetics of being a poor scholar but the admiration gained by attaining educational credentials did not necessarily translate to financial success and stability. The only way to ensure that your entry into the aristocratic class was also financial fruitful was to obtain the elusive jinshi which meant an enormous influx of prestige for your clan and official appointment which brought with it income and entry into the ruling scholarly class.

As I mentioned before at the beginning of my answer, the class was also not really based upon guaranteed hereditary privilege. This is especially true of clans who were a part of the actual, ruling scholar-elites. The enjoyment of the privileges and relative wealth of this class was never a sure-fire thing and it was definitely possible for families to lose their foothold within the class. Whether it be by political intrigue or just something as simple as failing to produce family members in later generations who could pass the examination, there are definitely examples of clans and families who fell into destitution following runs of bad luck. But on the flipside, families absolutely could and did rise from obscurity into the aristocracy thanks almost exclusively to high placement within the examination system. A perennial recommendation I make is Ho Ping-ti's The Ladder of Success which, while admittedly a bit dated, still is one of the few (arguably definitive) works of social mobility as it relates to the imperial examination in the English language.

The Qing and Ming dynasties also had more 'traditional' aristocracies as well which were not strictly tied to 'landed' status but within these realms, my knowledge is definitely much more shaky. I'm sure someone else might be able to give you a much better run-down of the Qing banner system.

I have written more about the topic if you're interested:

Ming bureaucratic efficacy

The examination

Yes you are right. Many of the countries that had Aristocracies based it predominantly off of the land they held. Usually the more land they held, the more powerful the Noble, hence why they were so significant. I will answer the question but a bit of extra context I guess. Nobles and Aristocrats, in general (the British aristocracy poses 0 threat to the current British Government for the most part), have usually been seen as a threat to whoever the ruler of the nation was as many of the top Nobles/Aristocrats commanded an extensive portfolio of land and wealth which could compete with the sovereign ruler either by themselves or in a coalition with other Nobles.

In your study of the English nobility you will at some point come across King Henry VII (R. 1485-1509) who spent a great deal of time and consideration trying to limit and use the Aristocracy to enhance his own power. If you are researching the Nobility and Aristocracy he is a very interesting case study.

I can think of a couple of “Non-land” based Aristocracies that have popped up from time to time across history. It does depend on how loose your definition of an Aristocracy is however. First group I might argue are the large Southern slave owning Plantation owners in the build up the the American Civil War who profited off of the use of slaves in mass agriculture, usually cotton. They didn’t have titles or the social status that many Aristocrats in Europe and elsewhere had. They were simply business men (of one of the more abhorrent and vile industries the world has ever seen). However, they did have the political power that many of the more established “Old World” aristocrats had access to in their respective eras (at this point in the 19th century the aristocracy wasn’t a massive thing in a lot of places anymore). The large plantation owners were a relative minority in the South. By 1860 only 25% of Southerners owned slaves and around 5% of the Southern population had access to the good farmland suitable for Mass cotton (and other crops) growth. In total there was around 10,000 families in the South that owned most of the slaves. Being a large plantation owner was a rare profession. They had access to large swathes of political and lobbying power. They were able to Lobby the US government for decades prior to protect or grow their awful institution. They had so much power they were even able to challenge the US government, as seen in the Confederate secession in 1860. Of the 50 representatives that met in Montgomery to secede from the Union, 49 of them owned slaves, with 21 of them owning 20+ slaves. They were able to challenge and wage War with a significantly more industrial North for 4 years during the Civil War, funded predominantly by the Slave plantations. They had the Wealth and the political power to be called a “Slave Aristocracy”. I will concede that they did own large swathes of land which is where they made they profits through the horrendous exploration of African American slaves so they could arguably be “land based”.

You could also argue that many of the large American Industrialists at start of the 20th Century during “The Gilded Age” could be argued as Aristocratic. People like Rockafella and Carnegie amassed such an absurd amount of wealth they became a social elite. Wether that is an aristocracy is up for debate.

Even if you look at the world in the modern day you can find argue there are a few examples of “non-land” based Aristocracies. Places like Russia have a group of extremely powerful men who amassed their wealth from Industry called the Oligarchs. They have a lot of social, financial and Political power within Russia. Even on a less serious note you could possibly argue that celebrity culture in places like the US are a form of aristocracy. Families like the Kardashian-Jenner family have huge amounts of wealth and social currency. They have even began lobbying the Government.

Those are a couple examples I could think of and I hope that helps. There are definitely a lot more, especially in recent history and the modern day where people amass wealth through industry, not land.