S.Arabia has a lot of toys, but there isn't much evidence they know how to use them. I agree with you on Italy, I overrated them. There should be an asterisk next to Russia as well. Give 3-7 a couple years build up and I think any one of them could embarrass the Russian military....assuming it doesn't go nuclear.
This is "power and influence". You're right that SA hasn't shown that it can use its military toys, but it has great influence through its funding of right wing religious groups across the world. This influence is not just in the Arabian peninsula - SA was a major factor in Pakistan changing from a somewhat secular Islamic country to a more theocratic one, and of course there is the Taliban and Salafist mosques across the former SSRs (for starters).
I would even consider pushing SA into the top 10 based on its religious influence.