Their link to the "official site" goes to the overall main page for the Mobile series. I admit I can't find any page for Material Dungeon itself on Namdai's site, but the game does exist in reality. I remember someone showed a legitimate magazine scan of this game on the Tales forums as well, granted it was several months after release and people were questioning why there was an entry for it on Wikipedia. The magazine scan was proof enough to convince me to make the page on our wiki in the first place, with what little info we knew. I don't remember what thread that would have been in though.
It calls it Tales of the World: Material Dungeon. Should I put it as both World and Mobile? Also, forgive me if I'm wrong, but the screens look like a Narikiri Dungeon done as a roguelike, but I can't read, so can you confirm?
If by "roguelike" you mean that battles are done on instanced dungeon maps without separate battle screens, so exploration and combat are done without transition, then yes that's exactly what this game looks like. The text only says it's a turn based system, which means it's probably similar to NariDan 3 dungeon movement, with more of a hack-and-slash aspect due to what seems to be the lack of an LMBS.
As for the "world" thing, yeah it really should be "Tales of the World: Material Dungeon", as it's listed this way also on Wikipedia and on the Tales forums. It's still a Mobile game, so there's no harm in adding it to both listings.