Heroku's buildpacks make some default assumptions regarding an app's startup. For a Ruby on Rails app, for example, it would simply start the web server using `bundle exec rails s` unless you define something else in the Procfile. I'd assume there is a similar procedure for PHP apps, probably starting an nginx instance and pointing it at the app's index.php or something like that.
The way I understood it, app.json is there to customize the environment for the application to run in – providing ENV variables, required addons (think databases, memcache, etc.) and pre/post deploy scripts. A sort of configuration-as-code if you will. It is explicitely not used to define the actual processes that should be started when the app is deployed, that's what the Procfile is for, as long as you're running in an environment that supports Procfiles.
I'm not really sure what to tell you regarding vendor lock-in. Apart from the app.json the repo itself looks completely vendor-unaware, as it is simply a PHP application. It doesn't seem to make many assumptions regarding your (local) infrastructure but rather assumes you know how to get a PHP application to run on your server/computer. The presence of the app.json file is just an affordance to those who would want to try out the app without having to configure anything themselves.
On the contrary, now that I think of it. I always found Heroku to be rather non-locking, as you can just take your code and run it somewhere else. You need to provide some additional tooling around your deployments yourself in those cases, but that's true for all PaaS providers, isn't it? Heroku Addons are nice features, but usually simply services provided by third parties that are made available using automatically generated ENV variables, which you could simply copy over to wherever else your app is running.