The issue with your animation is that the Art-board and the animation itself are quite small. So, when you export as video, the video player enlarges it by default, causing it to look very pixelated.
You can try two things:
Try exporting in a different format, depending on what you need the animation for. E.g. if you need it for a mobile app, you can export a Lottie JSON, or if you need it for, say, a website, you can export for React, Vue, etc.
If you really really want a video, in a quick and easy way, I’d suggest going to your animation's share page (you can get the link from the Publish modal), zooming in on the browser (it won’t pixelate), and use a tool like Giphy Capture to shoot a video of your screen. It will look as crisp as you need it!