I'll try and explain what I think, but I am not sure I am going to explain it well enough.
This is Windows 7. Going back to the time of Windows XP, when the computer arrived with the XP OS installed, (or when XP was installed by the user), the first time the user logged on was with XP's own System Administrator account. That's what I call it, System Administrator, because other accounts were either just Administrator or Limited accounts.
The unwritten rule then was, create your own Administrator account immediately and never use that System Administrator account. Then log in using the newly created Administrator account, and 'immediately' create a 2nd spare Administrator account.
Why do all this? As soon an Administrator account was created, the XP's own System Administrator account disappeared from view. it would not show up on the Welcome Screen and could not be used, except through Safe Mode. Then you, the user, would use your own created Administrator account. Why create the 2nd, spare, account? because if your own account became corrupted in any way, you could, at least, log in by using your 2nd Admin account to repair it, or at the very least, to salvage your files. With the hidden System Administrator account you had a double backup available.
So many times in these forums we saw posts from users who had never created any other Admin capable accounts and were using the System Administrator account. That account then became corrupted, and they were stuck, and locked out, and could not get back in. There is little help that can be offered in that situation.
But that was Windows XP. You are using Windows 7.
Microsoft changed this in Windows 7 and this is confusing with what you have said.
Microsoft changed it that, when Windows 7 was installed, the first time you the user logged in, Windows 7 would force you to create your own Admin capable account. Then the Windows 7 System Administrator account would hide itself.
What I think has happened to you. There are two scenarios;
1] You are, somehow, using the System Administrator account and have never created your own Admin capable account. I don't know how that is possible. Someone else has come along, created an Admin capable account and this has automatically hidden the System Administrator account. You then come along, start the machine (I assume no account has any passwords), and the system boots directly into the new account. Some aspects are common to all accounts, eg Desktop background, and so on. Possibly even, the game you were playing was copied to the new account, but not any saved games.
You play the game, shut down the computer, and then someone comes along, logs into the hidden System Administrator account, and deletes this new Admin capable account. You return, start the computer and it logs straight into the System Administrator account.
2] That System Administrator account is about to get corrupted. It disables itself, and the only other account available is some non-Admin Guest account. Desktop background is the same, and that game is available, but not any saved games. You play the game, shut the computer down, then when you next turn it on the System Administrator account is, somehow, working again.
Those are the two scenarios. I can't tell which, or whether there are any others, because the information you provide is limited. I asked questions in my first post and they are all unanswered, so my responses are limited to wild guesses.
Hope that helps.