With Videogular you have all those requirements covered. Probably you need something pretty basic like this:
http://www.videogular.com/examples/simplest-videogular-player/
You can fork the codepen and add the loop capability. To do the fullscreen on play you can add an ng-click to the vg-overlay-play plugin with an API.toggleFullScreen() for example.
HTML
<div ng-controller="myController as ctrl">
<videogular vg-player-ready="onPlayerReady($API)" vg-loop="ctrl.config.loop">
<vg-media vg-src="ctrl.config.sources"></vg-media>
<vg-overlay-play ng-click="API.toggleFullScreen()"><vg-overlay-play>
</videogular>
</div>
JS
angular.module("myApp").controller("myController",
function myController($sce) {
this.API = null;
this.config = {
loop: true,
sources: [
{src: $sce.trustAsResourceUrl("http://static.videogular.com/assets/videos/videogular.mp4"), type: "video/mp4"},
{src: $sce.trustAsResourceUrl("http://static.videogular.com/assets/videos/videogular.webm"), type: "video/webm"},
{src: $sce.trustAsResourceUrl("http://static.videogular.com/assets/videos/videogular.ogg"), type: "video/ogg"}
]
};
this.onPlayerReady = function onPlayerReady(API) {
this.API = API;
};
}
);
I've not tested this, but it should work or close to.