No, rivers and other land-based sources account for 10-12%
Sources of ocean-based plastic pollution
Almost 90% of plastic debris that pollutes ocean water, which translates to 5.6 million tons, comes from ocean-based sources. Merchant ships expel cargo, sewage, used medical equipment, and other types of waste that contain plastic into the ocean. Naval and research vessels eject waste and military equipment that are deemed unnecessary. Pleasure crafts release fishing gear and other types of waste, either accidentally or through negligent handling. The largest ocean-based source of plastic pollution is discarded fishing gear (including traps and nets), estimated to be up to 90% of plastic debris in some areas.
Source: Plastics in the Marine Environment: The Dark Side of a Modern Gift
This 2012 review explains a much smaller percentage comes from land-based sources:
Approximately 0.8 million tons annually of marine debris, which is 12% of the total debris input into the oceans, originates from land-based sources, and primarily consists of discarded plastic items (user plastic). In highly populated areas, marine debris comes primarily from the land.
So what about that study?
The study — Export of Plastic Debris by Rivers into the Sea — says in its abstract (emphasis mine):
We analyzed a global compilation of data on plastic debris in the water column across a wide range of river sizes. Plastic debris loads, both microplastic (particles <5 mm) and macroplastic (particles >5 mm) are positively related to the mismanaged plastic waste (MMPW) generated in the river catchments. This relationship is nonlinear where large rivers with population-rich catchments delivering a disproportionately higher fraction of MMPW into the sea. The 10 top-ranked rivers transport 88–95% of the global load into the sea.
In other words: they did not examine the ocean, they examined rivers. And their number does not say that 88-95% of the plastic that has ended up in the ocean comes from these 10 rivers, but that of the Mismanaged Plastic Waste that rivers in particular contribute to the oceanic plastic pollution, these 10 rivers account for 88-95% of that contribution.
But(!) as the study above says, rivers and other land-based sources of oceanic plastic waste account for 10-12% of the total plastic waste in the ocean.
@MadScientist concludes that the Wikipedia quote may be erroneous, and the 90% figure may be off by a bit.
This however does not change the fact that Export of Plastic Debris by Rivers into the Sea does not deal with all plastic waste that end up on the oceans but only that which arrives by river.
This — by all means — strengthens the original claim that it is in all likelihood not "your" straw that ended up in the nose of this unlucky turtle unless you were carelessly discarding it directly into the ocean or nearby that. Never the less the facts stated are misinterpreted and rivers are not the only and probably not even the majority sources of plastic pollution in oceans as a whole other than in the immediate vicinity of where rivers discharge into the sea.