This second video looks briefly at the time trail mode (a racing mode, essentially), where you can beat the clock on two stages (the 3rd crashes the game), and these scores were going to have online rankings, by the looks of it.
This is followed by a death match (much like a first person shooters multiplayer mode) which has options for split screen up to 4 players, as well as online play and link up play (very few games even used this)! Not sure if the link play works, but the online obviously will not.
Finally there's some footage of a glitch I came across. If you save the game in story mode when it prompts you to at one point, loading the game up makes you falls and get stuck for some reason. You can prevent this by holding the R trigger when it loads to fly forwards before you land in the area that makes you stuck.