A newspaper said in 2080 China can be a developed country, with a bigger population. Does that mean China's GDP is going to be bigger than the USA's and Europe's combined?
Also, is this possible even though China's land area per person is smaller?
This depends on long-run economic and demographic trends that are very difficult to forecast.
That said, the medium fertility scenario in the UN's 2012 World Population Prospects puts the population in 2080 of China at 1173 million, of Europe at 659 million, and of the US at 446 million. Since the combined population of Europe and the US, at 1105 million, would be only slightly below the population of China in this scenario, China's output per capita would have to be more-or-less completely caught up with the average in Europe and the US in order to exceed their combined GDP.
Although this would be a very strong performance, it is certainly plausible given the experience of China's neighbors: Japan, South Korea, Taiwan, Hong Kong, and Singapore all have per capita GDP within the range of other developed countries, despite all starting far behind the US and Europe as recently as World War II. (Japan had already experienced breakneck development following the Meiji Restoration, but according to the Penn World Table it was far behind the US + Europe average after World War II, and according to Maddison this was not just a result of wartime destruction: Japan was still far behind even before the war, at maybe 40% of US GDP per capita. Its performance following the war was therefore quite remarkable. Of course, South Korea's performance - starting at roughly the same level as sub-Saharan Africa - was an order of magnitude more impressive still.)
Large-scale economic and political changes will most likely be necessary for China to achieve convergence to Western output per capita, but 65 years is plenty of time for these to happen. 65 years ago, in 1950, the Communists were just wrapping up after victory in the Civil War; 65 years before that, in 1885, the Qing Dynasty was still sputtering along.
One consideration that will likely not matter much in all of this is land area. First of all, China's population density is actually lower than that in many of the world's leading economies - Japan, South Korea, Taiwan, and Singapore are all far denser, and the UK, Germany, and Italy are somewhat denser as well. Second, very little of the output in advanced economies depends on land area and natural resources: for instance, in the US, agriculture, mining, and resource extraction combined are about 4% of GDP.
Of course this is is possible. China is a very large economy currently and it is likely quite a way away from reaching its production frontier. It has lots of room to grow.
A lot can happen in 65 years and any forecasting this far into the future will be subject to a high degree of error. Don't forget that the US and Europe are dynamic as well. The current world economic climate may be in China's favour now but in 65 years who knows. Maybe everything we will need can be 3D printed an large scale manufacturing won't exist.
It is hard to look at The Next 100 years. It attempts to speculate on what can happen. *Spoiler*, the author does not expect the 21st century to be China's.