If I understand what you mean, you say something like running an installed application through a browser link, is it right?
Those that you need to visit the website and click a PLAY! button, so the application will run. If you try to run the game without going through the website it wont run.
Is that it?
If so, there are surely several ways to do so. One I can think of is the classic special link, like magnet links, steam links to name some.
For an example:
notice that this link is not http nor https, it is WeirdProtocol
If you try to open this link, your browser will tell you it can't open the link since there's no application configured to open such links, under the special WeirdProtocol protocol. This way, you can now deploy an application and configure it to open such protocol. This would allow you to run an application via a website on any computer where it is installed. Also, you can parse that link, passing any kind of information from the website to your application.
So, this would, in fact, run an application or game through a button on your website, given the game is installed on the machine.