Not directly or without a workaround. To play your locally stored videos natively from the AppleTV menu system you must use Home Sharing within iTunes that is running on a powered on computer.
Workarounds to using iTunes include:
1) Using an iOS device to play the video, the using AirPlay to push the video up to the ATV.
2) Using PlexConnect to "hijack" the trailers app, although this would require Plex Server running "somewhere", somewhat similar to running iTunes.
There may be other methods, but the above are most commonly used to bypass the need for iTunes running on a computer.
To reiterate:
To play your locally stored videos natively from the AppleTV menu system you must use Home Sharing within iTunes that is running on a powered on computer.