Jeez...
1. Don't confuse inventing a technology with making an innovative product.
XaviX looks like an innovative product in its own right, but neither it nor Wii invented a new technology. They both just applied old technology in new ways. The way Nintendo applied it, with a single standard controller instead of a bin of controllers, would have far greater chance for success, everything else being equal. Now, does Wii Sports ALONE look like a XaviX rip-off? Yeah, sort of. 
2. Nintendo was fooling around with electronic components in light gun toys in 1970. They owned light gun arcades dating back to 1973. They sold their first home consoles in 1975, as the Japanese distributors of the Magnavox Odyssey. They sold plug-and-play TV games in 1977, arcade machines in 1978, Game & Watch games in 1980, and released one of the most influential games of all time with Donkey Kong in 1981. Their connection to gaming prior to the NES was not some small thing.
"[Our former customers] are unable to find software which they WANT to play."
"The way to solve this problem lies in how to communicate what kind of games [they CAN play]."
Satoru Iwata, Nintendo President. Only slightly paraphrased.
