That is to be expected and I'm not sure why anyone would want it to be different. 1px lines are simply too thin even for HD or 4k video. You need to make them thicker so the antialiasing algorithms actuall have anything to work with. Otherwise you have to accept it as it is, including that this will flicker like crazy at the slightest bit of motion.
If you want to create 1 pixel thick lines in a video then you must perfectly align each line (path) with the pixel grid, make sure that the color compression used for your deliverable video can deal with the color differences without fouling up the color (MPEG h.264 colors is compressed in blocks of 4 pixels at best), and make sure that your video is always played back without any scaling. If you don't follow all these rules your line must be at least 2 pixels thick, 3 is better, four is best, and you have to live with antialiasing that happens when the video is played back at different resolutions.
The long and short of it is that single pixel thick horizontal and vertical lines are a very poor design choice.