No jacket or tie needed. Rules are no tank tops on men, no torn jeans, no swimsuits and no t-shirts with offensive pictures or language. That's it. Everything else is okay. It's not business casual. It's much more relaxed. Shorts are park wear and they are fine.
Disney tried to institute a business casual standard, which would definitely not include shorts on men or t-shirts! But it didn't work. So, both shorts and t-shirts are fine.