There is a dumb way to play the loop without a visual jerk - glue the multiplied loop clips and create a new big video file. But this is a breach of the loop idea - new video has the end!
I was dreaming about the loop DirectShow filter, but found none in Internet. So I left with this kind of smart way to play the loop:

Conditions
Windows (DirectShow).
Video loop format and container must be MPEG (and I mean not MP4, but MPG).

Tools
Elecard Codec SDK
http://www.elecard.com/download/#sdk
Specifically you need its sample application "NWServer", which demonstrates Elecard DirectShow streming filters capabilities. Everything about NWServer and what it is made of you can read in the nice Elecard Codec SDK Reference Manual PDF. There is a counterpart - NWPlayer and with some knowledge of DirectShow filters you could get a picture in any DirectShow player.

Settings
Set "Network" properties to UDP protocol, local IP address (I think 127.0.0.1 won't work, you will need to find out the real address of your NIC, which is visible in the "Interface" droplist), local scope.

Process
Open loop MPG in NWServer, set its network properties, start NWServer streaming. Then play.

Remarks
Well, I am using older Elecard Codec SDK and not tested the current downloadable version, but I am pretty much sure it will work.
Whatever player you choose (I use Zoom player with custom mediagraph) - use Elecard MPEG demultiplexer DirectShow filter.
GraphEdit or GraphStudio tool may be fun to make oneself familiar with Elecard DirectShow filters.
I needed DirectShow setting badly, but as non DirectShow alternative - I read that you may program the loop with AviSynth.