I'm not an english native speaker, but I never came across the word 'avaibilities'. A Google search for 'avaibilities' gives about 9000 results while 'availabilities' has 2780000 results. I'd guess it's a typo. And if I'd read it somewhere I think my brain would just interpret it as 'availabilities' and maybe not even see the error. But I'm curious what other people say who have more knowledge in languages.
Yes you're right. Definitely avaibilities makes no sense. I asked my english cousins and they agree with you guys. It's changed now