Watch the video. Even in your own video you added a caveat "as long as the tiles are sufficiently shuffled" and I don't think they were really sufficiently shuffled in your video.
Apply the same caveat to coins and you get 51%/49%
1% bias.
Also, the bias diminishes over turns, so it is basically negligible... Basically 0 for a 128 bit outcome.
Dice is similar. Dice may have some bias, but it's negligible after 128 bits.
Same for your paper, but I highly doubt that your solution is less biased than a common dice. The shuffle and tile selection is completely human, a dice is mostly randomised by gravity, unpredictable bounces and spins.
