I couldn't find a proper explaination, tutorial or thread online explaining the following: I "simply" want to load a Vimeo Video (where I have a pro-Account) without controls (play, pause, timeline, whatsoever) just the pure video (also without the black bar top and bottom) and stream it within a div I created. I want the video to be always fully filling this div.
How can I use the Vimeo-API to do that? I found examples of the Vimeo-API but nowhere I could find anything regarding loading the plain video file.
According to this answer, your Vimeo videos should have a "play in external player" link (Pro account required):
Go to your Video Settings and Video File, at the bottom there is a section called Use Your Own Player, you'll find there direct urls to your video.
You can embed that direct URL in a player of your choice - e.g. a <video> element:
<video src="http://player.vimeo.com/external/85569724.sd.mp4?s=43df5df0d733011263687d20a47557e4"></video>
You can create that <video> element using JavaScript, as well.
A plain <div> element can not dispplay video without some element to aid it.