Somewhat relevant might be these companies´ own opinions.
Nintendo has repeatedly reiterated it´s ¨blue ocean¨ strategy which is premised on not competing but instead operating in non-competitive niche.
I believe Nintendo has been successful as of late which would be strange to happen meanwhile the company is ignoring the supposed competitive reality.
To the extent there is competition, I think it is small element, and that could be said re: any consumer entertainment/hobby (ice-skating, alcohol, etc).
I think if Sony launches a hand-held that might open up more direct competition. But it could very well happen that they exist in separate niches.
Being classified as ¨video game console¨ doesn´t entail direct competition, no more than ¨home electronics¨ entails Nintendo is in competition with blenders.