Propaganda is a word that traditionally has negative connotations. It's not really a bad thing depending on what the message is, but there's little doubt it can be a powerful tool, and a dangerous one at that.
Propaganda has been instituted in posters, movies, cartoons, books, songs, and public speaking. The messages are typically heavy-handed, aiming to brainwash rather than inform or educate. Video games are a recent addition to the propagandist's arsenal.
Warner Bros. employed propaganda cartoons to build morale during WWII. Russia and Germany also used propaganda cartoons, but the tone was gravely serious. Propaganda is designed to influence, and it can do so in a variety of ways, through a variety of mediums. But no other medium delivers like video games. A video game can include the most effective elements of other forms of media, with the added benefit of interactivity.
Fortunately, the majority of video game enthusiasts worldwide are wise to such nefarious influences. Unfortunately, there is a huge demographic susceptible to such manipulation. People in oppressed countries, the uneducated, and those with fervent religious, social, and political beliefs are more easily manipulated. Stuff we would laugh at will be taken deadly seriously by the ignorant.
Propaganda video games do exist, including games designed to recruit soldiers for the U.S. Army. There are also games for Christians, Muslims, and the KKK.