Hello Dawney,
yes, Evernote is really capable and powerful. To give you an advice on how to use it for game development I would need more information on what you would exactly like to do in Evernote and which tools you would like to connect and for what purpose.
However, basically you can write down all your ideas in Notes, and organize them in notebooks, for example one notebook per video game you want to develop. These notes could be just only a few words describing the first idea of the game, or even a complete project management plan for the whole development of the game.
Evernote has also a special codeblock, which you can add to your notes for creating, or storing potential code for the game(s). You can add images from impressions or first drafts of your characters as well as links or documents from your research on e.g. a historical background of a game. Here you could also use the Web Clipper to import snippets or even full articles from websites to store them in Evernote and find them later for further actions.
For tracking of your projects (video games development) you can use the Tasks feature to set due dates and reminders for upcoming tasks to keep on track of the development. You can use also create tables to set and overview a budget or expenses. And so much more.
As you can see there are a lot of opportunities for you in Evernote and you just need to find your own workflow that suits for you.
And related to the integrations you asked for: Evernote has some integrations, or other way round other apps have add-ins to send information directly into Evernote. And when using automator services like IFTTT, Zapier, or others you can create also your own workflows for these.