Does anyone in Academia.SE know about Saudi universities?
First, let me answer about the reputation/ranking of Saudi universities:

I should warn you that Saudi Arabian universities have a reputation for "gaming" these rankings you are relying on.

What they do is pay researchers at western universities to accept a second affiliation there. This allows the Saudi university to list them as faculty and claim credit for their publications and citations and thereby boost their ranking. In reality, these researchers are rarely if ever present and do not contribute to the academic environment there. Perhaps they visit for a week and give a few talks, but they do not supervise students or teach courses there.

For more details, see this question and the links in it: What should you do if a co-author has an unethical affiliation?
The answers to this question also show how people in the west react to this.

So the reality is that Saudi universities have a very questionable reputation in the west, despite their good performance in international rankings. 

Note that I'm not saying these are bad universities, but simply that you should be wary of the rankings and the claimed faculty. Every university seeks to maximize it's reputation, but Saudi Arabian universities have a reputation for going overboard with this.



Now the second part of your question -- how does going to a Saudi university play into your academic career goals given that you want to end up in the US:

Generally speaking, moving to the US after PhD is much harder than before. This is my personal impression and is supported by data.

The main reason is that, after your PhD, you are evaluated on your research and your recommendation letter writers and connections matter a lot. Thus you want to have research exposure in the US and you want to have connections in the US and letters from US professors. The easiest way to do that is to be in the US. 
Before your PhD this doesn't matter so much, as you are evaluated on your potential. 

Another reason is that, as you move up the career ladder, positions get more and more competitive. This makes everything, including moving countries, harder.

Of course, countries like Canada and Israel are very close to the US in terms of research connections. So doing a PhD there will be almost as good as doing one in the US.

If you are having trouble getting into a PhD program that you want, then doing a Masters is probably a good idea, especially if you get a good recommendation letter out of it. It isn't critical where you do a Masters.