What I want to know is whether it was the determining factor of their choice to surrender when they did. Would they have surrendered as quickly or at all without a Soviet invasion? Would they have surrendered as quickly or at all without the use of nuclear weapons? My reading of history is that even without the Soviet invasion they would have surrendered quickly (at most within a few weeks of when they actually did). Without the use of nuclear weapons they probably wouldn't have surrendered as quickly, though ultimately I think they would have surrendered before a land invasion of the home islands but after much greater destruction of Japan's cities and much greater loss of life of Japan's citizens.
As to the point of the Soviet amphibious invasion capability: conquering a sparsely inhabited island with few fixed fortifications hardly is not in the same league as the battle of Okinawa and D-Day. The Soviets might have been capable of taking Hokkaido, but the US and UK were capable of taking Honshu, and they had the recent experience to prove it beyond a doubt. I'm sure the latter fact weighed much more heavily on the Japanese mind at the time.