Strictly, a first party title is a title published by a first party. All the titles on that list are not only published by Nintendo, those IPs are owned by them (Nintendo has never published new IP without retaining control over the rights). The Last Story IP is owned by Nintendo. A third party published it in North America with the approval of Nintendo.
This argument has never made sense to me because it's always been divorced from reality. Whenever I hear that Nintendo hasn't delivered new IPs since Pikmin I automatically assume this person either stopped following Nintendo immediately after the GameCube launch or they live in a state of denial. Since Pikmin Nintendo have added a very large number of new first party published and owned IP to their catalog. The list is immense and includes, but is not limited too:
Eternal Darkness Golden Sun Chibi Robo Trace Memory Hotel Dusk Wii Fit Wii Sports Brian Age Endless Ocean Rhythm Heaven Xenoblade The Last Story The Wonderful 101 Nintendogs Elite Beat Agents The Legend of Starfy
Not to mention all the previously Japan only franchises that made the jump to international markets like Fire Emblem, Custom Robo, Advance Wars and Animal Crossing and new "sub-franchises" like WarioWare, Nintendo Land, Excite Truck/Bots. It seems that the only thing tired and in need fresh thought is this argument.
Master_Hermes' comments