Respond to HR the same way you responded to the manager.

Check your employee handbook to see if there is any guidance on using the computer for personal reasons during work hours, and if games are explicitly prohibited. (At my work playing games on the network is a firing offense because of potential danger to the network.)

You can probably expect a written final warning to never play games. And then never use a company computer for anything other than work.

Possibly. (Didn’t your mother ever tell you to never play video games at work??)
Be honest with HR and tell them the truth. But don’t let it happen again!

Do you have a union where you work? If so, there are going to be steps that will be taken before they can fire you.

Hopefully you’re a good worker and so that may help your cause.

Being finished with your work is not a reason to do something not work related. What you should do, if you’re finished with your work, is tell the boss that you’re finished and ask if he or she has anything they’d like you to do. I am aware that not many people may do that, but my point is that just being finished with your work doesn’t justify doing what you want on company time.

I’d fire you. Installing 3rd party software on a work machine could compromise the entire network of your company (I’m surprised you had the credentials to do so). For me it’s less about the fact that you were being paid to do work and you were fucking around, and more to do with the extreme lack of common sense. The fact you had administrative privileges on your computer may mean your company’s IT is so sloppy that they may not realize how risky doing what you did was—that could actually play in your favor.

If I were you, I would be honest, frank and say something like, “I know what I did was wrong, and I understand if you decide to terminate my employment as a result. My behavior was inexcusable, and I can guarantee that it will never happen again, should you decide to allow me to keep my employment. I like my job, this company and my team. I know that I am a valuable asset to this company, and I hope you will allow me the opportunity to make up for my poor choice and prove that to you.”

With the Notice to Explain, they’re going to want all the details. When did you install the game? What did you do when you finished your work? Why did you play the game on work time? Make sure your answers are logical and honest. It’s very likely they will know the answers before you answer them, because they will very likely know exactly what you’re doing with the computer every time you’re logged into it. Therefore, if you lie, they’ll know right away.

Be honest, be humble, be contrite.

Then tell us what happened!!