I was talking with a friend about Yamuachi's passing. We got on the subject of how much power and influence he still had at Nintendo. How will his passing on affect Nintendo's leadership and direction going forward?

Nothing.
He quit 11 years ago.

0%

He was a major investor still, was he not? Depends on where his shares go. Likely a wife or child would be just as unflappable as he was (helping to create Nintendo's near absolute immunity from investor pressure), then nothing will change.

It won't affect their leadership at all...

Pressure is on Iwata to enact his will, and prove his direction to any nay sayers, Yamauchi chose Iwata after all

Yeah he was a major investor. His family owns the company. IIRC he and his daughter were estranged. He made sure she wouldn't get hissares because it was feared she'd sell them to spite him.

Naturally, Hiroshi Yamauchi's wealth and shares will be inherited by his eldest son: Shigeru Miyamoto.