The source of this claim is a press release published by UFZ, a member of the Helmholtz Association, a German scientific organization. UFZ does environmental research for Helmholtz and is based out of Germany. Overall, this is a reliable looking organization based in research. The claim they make is “The researchers have also calculated that the ten river systems with the highest plastic loads (eight of them are in Asia and two in Africa) - areas in which hundreds of millions of people live, in some cases - are responsible for around 90 percent of the global riverine* input of plastic into the sea.”
From Nature, a leading international scientific journal:
“The top 20 polluting rivers were mostly located in Asia (Table 1) and accounted for more than two thirds (67%) of the global annual input while covering 2.2% of the continental surface area and representing 21% of the global population. Furthermore, the top 122 polluting rivers (4% of total landmass surface area and 36% of global population) contributed for >90% of the plastic inputs with 103 rivers located in Asia, eight in Africa, eight in South and Central America, and one in Europe.”
https://www.nature.com/articles/ncomms15611
It seems that 90% or more plastics in the ocean come from rivers, but not specifically from 10 specific rivers only.
From the Ocean Cleanup, a non-profit organization seeking to work to remove plastic from the oceans:
“Rivers are a major source of plastic waste in the oceans. We estimate that 1000 rivers, represented by the red dots, are accountable for nearly 80% of global annual riverine plastic emissions, which range between 0.8 – 2.7 million metric tons per year, with small urban rivers amongst the most polluting.“
https://theoceancleanup.com/sources/
There seems to be differing numbers of the exact number of rivers that the majority of ocean plastic comes from, but most research I came across seemed to agree it was more than 10 rivers. So while this claim is somewhat true, that >90% of ocean plastics come from rivers, it does not seem like it comes from 10 rivers precisely.