Regardless of sales numbers (assuming that what mysticstylez said is true, that if a game company has X amount of units at launch that company can expect to sell X amount of units at launch) the Wii has won the first battle because every single person I have shown it to has laughed their ass off while playing it and had a great time, every single one of them (from my mom, to my 9 year old cousin, to my nintendo buddies, to my pc/sony/xbox 360 buddies to my friends that never play any video games at all) has come back for more. Every single one has said that they HAVE to get one.
The PS3 has not even been mentioned inside my house unless we are discussing how appalling the idea behind the system is and how poorly it's been rolled out.
Nintendo has easily created the highest level of demand between the three systems this holiday season, and thats what they have won the first (of many) battles. Now we just have to wait and see what comes with the next wave of software.
Edit: Just wanted to clarify that the Wii has not won because every single person I personally have shown it to decides the fate of the video game industry, just that this is going on all over the country. Friends that have moved away but I still keep in touch with have talked to me about how all their friends get together, just like mine, to play.