Getting "fatal: this operation must be run in a work tree" after initializing a remote Git repo

I am super familiar with using Git on GitHub, but I am not at all familiar with git pushing to a custom machine instance.

I just figured out how to initialize a remote repo like this, last step being that I need to create a git init --bar "placeholder" thing on the remote server, under ~/project.git.

Then I went ahead and did this locally:

git remote add google example.us-west2-a.project:project.git
git push google master

And got the famous:

Enumerating objects: 4, done.
Counting objects: 100% (4/4), done.
Delta compression using up to 8 threads
Compressing objects: 100% (2/2), done.
Writing objects: 100% (4/4), 433 bytes | 216.00 KiB/s, done.
Total 4 (delta 0), reused 0 (delta 0)
To example.us-west2-a.project:project.git * [new branch] master -> master

Now, when I cd project.git on the remote machine, I notice it's similar to the .git folder inside my local project. And if I try to git status, I get the message:

fatal: this operation must be run in a work tree

So what do I do? I want to do a git push locally to push the contents of my git repo to my remote server, but I don't see any contents. How do I get and use the contents on the remote server? This way, I can then cd project on the remote server, and do node server to test out my node app. Later on I can do a git post-push hook or something, like Heroku does, to deploy a new version of the app.

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