I checked the Install Log in my Dead Space's Install folder. I noticed it said:
17:35:33 ERROR: Windows IGameExplorer is unable to AddGame (80004005)
17:35:33 ERROR: Attempt to retrieve GDF GUID failed (80004005)
17:35:33 GameExplorerInstall returns 80004005
17:35:33 ERROR: Failed to install 'C:\Program Files\Electronic Arts\Dead Space\GDFBinary_en_US.dll' for install path 'C:\Program Files\Electronic Arts\Dead Space\'
17:35:33 Failed to install GDF
17:35:33 Installer finished with exit code: 3
17:35:33 Shutting down data reader.
I found a solution.
Excerpt from the above link (solution is for Dead Space 3 but works the same for Dead Space)
To fix this you need to create a registry path called C:\Program Files (x86)\Origin Games\Dead Space 3\
1. Go to your start menu and in the searchbar type RegEdit and click on the program listed, alternatively you could use the "Run" feature.
2. In RegEdit, use the Folder Explorer on the left to Navigate to Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\EA Games\Dead Space
3. Right Click anywhere in the panel on the right and press New > String Value Name it "Install Dir"
4. Right click on the new value that you created and click "modify"
5.Type in C:\Program Files\Electronic Arts\Dead Space\
Note: if the error message in YOUR InstallLog pointed to a different folder, type that one in instead.
You are done! Close RegEdit, don't worry it will be saved automatically. The play button should now appear in your My Games section of Origin.
On a side note: Many people say that editing the registry can be dangerous. You shouldn't worry too much because you are just making a small change in it. Just don't run around RegEdit and delete every value that you find