IdleWild (Idle Wild) from Windows Entertainment Pack 1, 2, and 3. This is the latest version.

This is not a game, but a screensaver program. It originally came with Windows Entertainment Pack 1 for Windows 3.x, and was later updated in WEP 2 as well as WEP 3. Screensavers were necessary on older monitors to prevent damage, but not anymore. Despite that, people still like to use them.

8 screensavers were added in WEP 2 and another 8 in WEP 3. I counted the number of screensavers in this list and there are 24 total, including "Random".

The following was copied from Help - Overview:

IdleWild is a screen-saver application.

If you are away from your computer for a period of time and your monitor remains on, there is extra wear on your screen. A stationary image on your screen can "burn itself into" your screen and leave a permanent "shadow." IdleWild solves this problem by putting a moving image on your screen when you are not using it. IdleWild checks to see how long it has been since you typed something or moved the mouse. After a predetermined length of time, it replaces whatever is on your screen with an animated graphic of your choice. When you move the mouse, click any mouse button, or press any key on the keyboard, your original screen returns. (Although you may have to enter a password first.)

When IdleWild changes, or "blanks" your screen, it does not affect the applications you have running. It simply adds a patterned image on top of them.

Note: If the active window is running a DOS application or a Microsoft tutorial, IdleWild will not blank the screen, because it is unable to keep track of the "idle" time in these situations.