Anima Paper

Anima Player is an incredibly lightweight and straightforward piece of software that might just answer your prayers if you have always wanted a live desktop application that doesn't cost a thing and it isn't riddled with annoying ads and what not.

Works well on the latest iterations of Windows and comes with support for a broad range of video formats

Here's what you should know right off the bat. First and foremost, know that it's mainly intended for Windows 8 and 10, and, even though it has a special "Windows 7 and below" option, successful results are not guaranteed.
More importantly, it works with the most popular video formats out there such as MP4, AVI, WMV, MPG, and even GIFs. Also noteworthy is the fact it allows you to enable or disable the sound or the videos, as well adjust the volume.

Simple and efficient, little app

Regarding accessibility, we can point out that the application does not require installation,  it can also be minimized to the tray, and that its interface is on the you-cannot-get-it-wrong side of things.
That said, just browse for a video and load it from its destination and press the "Play" button to get things going. As expected, the video automatically starts looping until further actions on your part.

Should be treated with sympathy rather than criticism

There's also a "Run at startup" option, but, probably even more useful is the fact that it comes with support for multiple monitors. While we're on the subject, please keep in mind that this project is still in its infancy and that various features might still be a bit "flimsy," the "Multiple Monitor" feature included.
Nevertheless, the project itself shows great potential for future development, and we have especially liked the fact that we haven't encountered any types of really annoying issues, crashes or monitor flickering during our tests. We're not going to lie, CPU usage could be lower, but this issue can potentially be solved with proper optimization.

A few words about what you should expect with future updates

To end with, yes, we know what you're thinking: with a bit more development time and some good ideas, this project could become one of the best live desktop apps out there, and we totally agree.
As the developer points out on the app's official GitHub repository page, in the future, we might be in store for features like library management, automatic background changer with scheduling capabilities, and YouTube streaming directly on your computer's desktop. Fingers crossed.