Anything anyone says in this thread is pure speculation. No one can know exactly why Impact built or played the way he did because it's never been done before in the toplane, and much of what he did was unprecedented. With that said, speculation is good, since it can look into things to see how they work out.

So the health item, in this case Bami's Cinder: my best guess is that Impact felt threatened by the all-in of Gnar. Since mini Gnar is ranged, post-6 at high rage a Gnar can autoattack or boomerang to break Yasuo's shield, then jump in, transform, and ult for a substantial burst and potential kill, even if the Yasuo has high health. This is Gnar's typical strategy against squishies, particularly melee squishies. Buying armor is less efficient than health on Yasuo against this because his health pool is so small (and his shield is easily popped and avoided by ranged champions), so a health item is the way to go.

Assuming you want to invest some gold into HP, it seems like a ruby crystal or a couple of Doran's won't be enough - that's just one or two more autos from the Gnar and not likely enough to dissuade the all-in, so more investment is required. This means Giant's Belt or Bami's Cinder.

The difference is Giant's Belt gives +80hp, but Bami's Cinder gives the 5 (+1/lvl) damage per second in AoE, which does 50% bonus damage to minions and monsters. Traditional thinking here would say probably Giant's Belt, but some other factors can come into play: what about the possibility of Gnar stacking armor? Then the magic damage has more value. What about Yasuo getting more shoving power? Gnar in mini form has a hard time pushing waves, so maybe Impact was looking to shove in the Gnar and force him to cs under turret so that he could provide his team with more pressure on the map.

The big thing, I think, is that Impact was significantly ahead from the level 2 trade he was able to get. Knowing he was ahead, he probably didn't feel the need to finish a defensive item, so even though Giant's Belt builds into a better item (Randuin's is certainly stronger than Sunfire), he wasn't likely to need to finish it and would prefer to build damage to help extend his lead in the lane, rather than building defensively and trying to stay even. Thus, particularly since Bami's Cinder passive scales with level, it's a little stronger later on as a single item than Giant's Belt for pushing in particular. While it's a little worse against burst damage, Impact wasn't too concerned with needing to live since TiP's team comp provided a reliable knockup from Fizz so he wouldn't need to do it himself, which requires sticking in the fight for an extended period of time.