In 1292, Marco Polo was waiting for the winds to shift so he could leave Sumatra and return to Venice. He spent his time learning about an island called Java, in the southeast. Everyone said that it was the largest island in the world, it had a great king and was very powerful. It has vast sums of wealth and its great spices. (https://www.youtube.com/watch?v=bZKHATDgPO0)
The Java we know today is definitely not the largest island in the world. However, Australia could be categorized as the largest island of the world. The Sumatrans obviously knew that Sumatra was bigger than Java. Were they perhaps actually referring to Australia?
First of all, Australia was known far before Europeans arrived. Papua New Guinea, Sulawesi, Srivijaya, China, Tamil kingdoms and even African Islamic kingdoms have traded with Australia! Even coins from Africa were found in Australia(http://www.digitaljournal.com/article/350471)!
So, were the Sumatrans referring to Java or Australia?
As a counterargument, Java IS the largest island in the world… population-wise. I don't know if it was as populated as it is now, though.
As you mentioned, Java is the next island to the Southeast of Sumatra. It is not larger than Sumatra in square miles, but even in Polo's day had the heaviest concentration of population in all of what is now Indonesia. This made it the cultural center of the region. It had the largest population in 1AD, and contains the capital of Indonesia today.
Australia was in fact physically larger, but was very sparsely populated. According to McEvedy and Jones, it had at this time a population of about 200,000 hunter-gatherers spread over the area of an entire continent, while Indonesia had around 5 million, concentrated on Java. There's little evidence that Indonesians had any significant contacts with Australia, and there wouldn't be much worth visiting for.
So no, there's little doubt that they were in fact talking about Java when they told him about "Java". Sumatrans at the time would indeed have considered it the most important island in their world, and the biggest in population that they knew of.
Marco Polo was travelling with a large and well armed Mongol diplomatic mission, with a Mongol Princess travelling to marry the Ilkhan in Iran. No doubt the leaders of the diplomatic mission would have access to high level Sumatran leaders with information about countries the Mongols might consider invading. I note that Sumatran leaders might want to give the Mongols the idea that they should conquer Java before conquering Sumatran countries.
Did Marco Polo have such high level access or did he have to ask private Sumatrans he met?
The port where Marco Polo was in Sumatra may have been hundreds of miles from the nearest part of Java. The strait between Sumatra and Java is only about ten miles wide at the narrowest. Legend claims that an eruption of Krakatoa destroyed a former land connection between Sumatra and Java. The Sumatrans should have been very familiar with Java.
Marco Polo could have heard stories about the much larger New Guinea and Australia, also southeast of Sumatra, and mixed them up with the much more numerous stories he heard about Java. Or, if Sumatrans wanted to encourage the Mongols to invade Java instead of Sumatra, they might have exaggerated the size and wealth of Java.
Sumatrians living in port cities would have heard from sailors in shps from China, the Philiippines, India, Iran, Iraq, and Egypt, stories of the Mongol conquests of China, and Iran, and Iraq, and Mongol raids into India, and wars in Syria between Egypt and the Mongols. In short, they would have known that the Mongols had conquered a very large part of the world known to them in only a few decades.
I note that there should have been a number of larger and smaller kingdoms and states in Java in 1292. The next year, 1293, the Mongols invaded the Javan kingdom of Singhasari, and the lord of Majaphit helped them defeat Singahsari, and then turned on them and drove them away, founding the Kingdom of Majaphit in 1293. Majaphit would eventually rule all of Java and claim over lordship of all Indonesia.
Perhaps one or more Javanese Kingdoms in 1292 were larger and more powerful than any kingdom in Sumatra. And it is also possible that Marco Polo could have learned about the Shailendra Dynasty which fell in about 1025, 270 years earlier, but had been very wealthy and powerful.