Your NES game analogy is completely wrong. There is no licensing agreement for physical games, which is something I've had to beat into people's heads repeatedly.
Although this is a significantly different situation from the Big House/Slippi incident, it still comes down to the fact the game is being streamed for profit.
Nintendo has the right to shut down streams. They do not have the right to shut down the tournament altogether, although with the way the tourney scene works nowadays, unstreamed tournaments are nearly unheard of.
The Zelda series has an interesting history with hacked saves. The first major Wii exploit was distributed in the form of a Zelda: Twilight Princess save file.
EarthBound's soundtrack is a sampling nightmare, which was allegedly the reason the game took so long to be rereleased. (I say "allegedly" because Nintendo has denied this.)
Of course, the most obvious reason not to hotlink images is that you might end up Goatse'd.
All the other claims are basically throwing stuff out and seeing if it works, but the DMCA agent claim is huge.
Typo: "This week in 20011"
These days, are there any crowded theaters to yell "fire" in?