I am also considering creating a native app similar to CakePhp or Node.js.
As of this writing the latest version of PHP was released a mere 21 days ago -- certainly nothing 'outdated' about it!
My advice would be to not worry about the latest/greatest/most hyped up new thing, and simply go with what you know. You can make serious progress on your product much quicker if you stick with a stack you're already comfortable with.
I say all of the above as someone who doesn't really like PHP, too, for what it's worth -- choice of stack is much more about personal preference than any objective measure of what is 'best'.
I didn't follow some portions of your question, and hopefully you take this well :).
"I am also considering creating a native app similar to CakePhp or Node.js" --> There are three separate concepts in there that are worth unwrapping, so probably good to talk about that first:
CakePHP is a PHP framework, comparable to Symfony/Laravel/CodeIgniter/etc.
Native apps are usually iOS, Android, Windows, etc, but can be hybrid, too (Ionic, Phonegap, React Native, etc). Connected native applications usually have a backend, which is usually written in a language like the ones mentioned above, and usually with a framework written on top of it to accelerate development.
With that out of the way, let's tackle the main meat of your question:
Can PHP be used to create a platform similar to AirBnB, Ebay, Amazon?
Answer: Absolutely!!! Just one recent example is Slack, who's backend is build on PHP (LAMP stack). Check out this tweet where they mention their stack: https://twitter.com/SlackHQ/status/426469205005705217. Another good discussion on it: https://www.quora.com/What-web-framework-s-does-Slack-run-on.
One bottom line is that choosing a technology stack is important, but more importantly is the correct and effective development on the chosen technologies. I've seen both beautiful and horrible applications written in most languages. Much care needs to be spent architecting and developing the solution, always using best practices, and considering what's the right decision for the business at hand (hint: there's no silver bullet).
My suggestion: choose whatever you're more comfortable with. Also, surround yourself with someone that has created something of the magnitude of what you're aiming for, and ask for advice.
Happy to jump on a call, show you some examples of this, and answer any questions you have!