The main competition that all handheld devices have had - games consoles, mp3 players, cameras, and yes media/Internet tablets - is from phones, because almost everyone wants to have a phone on them, so there's little need to have an additional device. Devices have only survived where they've become significantly different from phones. So small PDAs/tablets have mostly disappeared because of phones, and instead we now have large tablets. MP3 players have some advantages such as people wanting more storage space or a separate device for battery life, but many people use their phones. Cameras have so far survived due to people wanting better quality for special occasions, or things like zoom, but this will likely change soon (especially if technology like Nokia PureView are any sign of the future of phone cameras).
So Nintendo have already been facing a squeeze from phones. I guess the problem from larger tablets is that Nintendo can't even differentiate by making the device larger. Does the 3DS XL have anything for web/email or general Internet access, or allow playing of music/videos? It seems to me an obvious thing for them to do would be to make their device into an Internet/media tablet itself, so they would no longer lose out, and still have the edge when it comes to gaming.
Why not. He said the Kindle, because he has one. Apple users always mention their Iphone or their Mac as their example (even when it's completely irrelevant for us to know the brand), when they're not the lead platforms, I don't see why we should pick on someone for mentioning a popular device like the Kindle, especially when they're talking about something they own.
Also, I'm baffled that of all the tablets out there, you chose the Kindle as your lead alternative.
ETA: Also I presume the OP meant the Kindle Fire, which is a tablet running Android, the lead operating system for mobile devices, rather than the more commonly known Kindle e-reader - I have no idea whether that could do any games.