Yes. It's backed by technology and mathematical algorithms.
It's technology will eventually make it the pervasive medium of transacting. Despite all the FUD you see today, this is inevitable. In all cases where a technology has emerged that makes any day to day activity exponentially simpler, it always has ascendance. In this case it will be the cryptocurrency with the most integrated payment ecosystem, a good, low fee, scaling solution and one which is decentralised. Precisely because Bitcoin was first, and most popular, it hit a brick wall scaling, but also because of this reason it is going to be the first to have real solutions - in fact they're already rolling out quite quickly and will leave a lot of the alts behind. And maybe it won't be Bitcoin, maybe it will be one of the others, or a combination - but it will be cryptocurrency. Hence the value of the leading coins.
And the maths makes it scarce. There can mathematically only be 21 million BTC, which means that if a significant chunk of global commerce is replaced with something like Bitcoin, there will be a lot of people needing to use it.
Is it backed by anything in the sense that you can go to the reserve bank and demand your equivalent value of gold? Nope. But neither is fiat money - that's why it's called "fiat" (the Latin word for "let it be done") i.e. it is what it is just because the government said so. To my mind there is a heck of a lot more backing cryptocurrency than arbitrary government decree.
Crypto is money because an irrefutable algorithm said so and thousands of distributed nodes agreed. And only so much can ever be circulated. Fiat money is money, because some (inevitably temporary) government said so. And they can print all they want. Fiat money has value only for as long as you have any faith in whichever government prints it. With cryptocurrency you only need faith in mathematics, and maths isn't really a matter of faith.