I don't think you've ever seen a good Renekton play that match-up. With proper wave control, Renekton can slowly shove the wave into Nasus and build an experience advantage and build enough fury to chunk Nasus for any CS he tries to take. After that, he can zone Nasus from farm and leave him exposed to ganks if he properly reset the minion wave and froze it on his side of the map.
Renekton has a signficant advantage in that match-up when both play it correctly since he controls the minion wave and early trades. While Renekton does get outscaled, he can use his early strength to build an advantage and keep Nasus down. Of course, this is assuming that both know how to play the match-up.
Taking a quick look at your recent Renekton vs Nasus game, you made many simple mistakes at a quick glance.
I would recommend:
[1] Rushing Black Cleaver instead of Ravenous Hydra
Black Cleaver provides early armor reduction for burst and extended trades while providing valuable CDR and health early-game. In addition, the Cleave passive on Ravenous Hydra (and Tiamat) ruins your ability to control the minion wave and freeze on your side of the map, which will leave you constantly over-extended and vulnerable to ganks or being chased down the lane.
Considering Nasus rushed Iceborn Gauntlet and Frozen Heart, the ability to reduce his armor would have been extremely valuable. This is especially true since he didn't have health to back it up until much later.
[2] Ward.
You placed 7 wards in a 28 minute game (while having a Yellow Trinket for the entirety of the game) and purchased no Vision Wards. This is abysmal and likely resulted in several deaths on your part due to your lack of vision and constantly overextending (since, again, you had rush Tiamat and Ravenous Hydra).
[3] CSing.
Your CS was 136 in a 28 minute game when you had counter-picked your lane opponent. Your CS was signficantly lower than it should have been, which resulted in you hitting power-spikes later than you should have and being behind in items throughout the game. Honestly, you should have had near double the CS you ended the game with.
Like I said before, Renekton controls the minion wave during laning phase. You should be last-hitting the majority of the CS in lane while zoning Nasus away from them with a proper freeze.
[4] Runes
AD Seals and Glyphs are useless. Don't bother with them since they are signficantly weaker than the alternatives.
Also, I'm not really sure why you bothered getting a Doran's Shield on your first back (or why you couldn't afford something better), but it wasn't a great purchase. You'd have more sustain and combat stats from hitting the minions if you'd purchased a Doran's Blade and the Block passive isn't really that useful against Nasus (since he doesn't really care to be hitting you frequently).