I agree that it was built around Arnold, but there is absolutely an extensive mythology there, in novels, comics, video games, a TV show, sequels, etc... We can agree that it's not as successful as Star Wars in the multimedia department, but there's a LOT of Terminator stuff to chew on.
All I'm really saying is... This franchise can totally survive WITHOUT Arnold, and without Sarah Connor, John Connor, or Kyle Reese. There are plenty of fresh stories to tell because it's such a rich, complex story. My concern with Genisys is that they're relying on stuff they've covered three or four times already - they're just shaking it up and calling it something else.
It's like any new item on the Taco Bell menu.... It's meat, lettuce, tomato, sour cream, and cheese on a tortilla.
The question you have to ask though is whether there is a Terminator mythology without John and/or Sarah Conner. Those two characters are the very reason for the events taking place. Once you remove them from a Terminator story there's not really a great deal to go off. I'm of the opinion franchising Terminator has never really made much sense because it's ben so dependant on those two characters and Arnold in order to survive. I think The Sarah Conner Chronicles is the only spin-off to work, mostly because it seemed like there was a conscious effort to keep the spirit of the first two films alive. The last 2 movies and now this one seem to have forgotten that.