I consider most anything to be copyrightable and therefore copyrighted as they are.
Images are copyrightable and therefore you cannot use these images without a proper license. If the license is not clear and explicit and allows the type of usage you plan in your game, you cannot use these images.
Per http://www.animatedimages.org/help.htm animatedimages does seem to grant some usage right that I could interpret as some open source license of sorts. At the same time, they (the animatedimages site) may not even have clear rights to some images as they state on their help page:
Where do your graphics come from?
All graphics offered by us have either been provided by our users or they were created or collected by our team. For images uploaded by our users, we have no control over the content. This applies both to the text and the graphics. If certain graphics or greeting cards infringe copyright laws or fail to meet our internal guidelines, please send us a quick note via mail.
Therefore, you are a bit between a rock and a hard place:
You could ask animatedimages for a clear open source license to some animated images to use in your game. But at the same time, they may not have clear rights to these and no ground to license these to you if they do not "own" them.
Your best course of action would be to contact them and/or consider an alternative source of media assets for your game.