One of the things I like the most about that animation is that it would totally be doable on real hardware... it would just cause major flicker with all the sprite tiles it would require. ^___^
I hate to be the bearer of bad news, but no, it actually isn't doable on the real hardware.
The flickering you see on the real NES is caused by sprites occupying the same scan line. In other words, if a sprite is horizontally within the same range as another sprite. This is common in NES games, and causes a little bit of slowdown in some cases. Fun fact: this is why most candles in the NES Castlevania games were placed where you have to jump and hit them, to keep them off the same scanlines as the player and ground based enemies.
However, that is not the only limitation for NES sprites. The NES has a 64 sprite hardware limit per rendered frame. The NES defines sprites as; 8x8, 16x8, 8x16 only. Those are the only sprite sizes available. This wouldn't make sense cause you would say "well Megaman/Simon Belmont/Samus/Mario/etc are bigger than that!". Yes, that is also true. Typically player characters in NES games are comprised of multiple sprites. Common platformer player sprite sizes are 16x32, 16x24, 16x16 because they are easily built by drawing anywhere between 2 and 4 separate 16x8 sprites.
Each log of the bridge would be, I'm guessing, at least 5-6 sprites each? And how many logs do you have there? at least 10? That's pretty much topping the limit already.
Sprite limits being hit don't flicker either. They just don't draw period, lag everything, and or crash the game outright. The flicker is only a scanline correction.