I don't think Spinarak or Ariados are Spiders... they have 6 legs. Spiders have 8. Probably explaining why it's not considered the "Spider Pokemon" under classification (They are the "String Spit" and the "Long Leg" Pokemon, respectively)
Except for the fact that this new spider, in fact, has 4 Legs. It's not like the kiddies are going to care much for biology.