I searched up different styles, and I say this style called Gosoku-ryū that has 46 katas including weapon katas. Why would there be katas involving weapons for a style of karate which is an art of the empty-handed?
Just because a karate style may include weapon katas does not mean that the name "karate" is invalidated. You can think of Kobudo as an extension, or sister art(s) to Karate. Okinawan weapon arts are supposed to have been based on farming tools that the practitioners would have had readily available.
Additionally, as has been noted elsewhere, Kara in the original characters for Kara-Te, may not have meant "empty", but rather "China" or "Chinese", referring to the Chinese origin of Karate styles. Take a look at Southern White Crane and compare to Goju-ryu, for example. Probably, the character was changed from Kara ("China") to Kara ("Empty") to remove the art from its Chinese predecessors. Therefore, in its original context, Kara-Te would have no seeming contradiction with weapon arts.