It's his secondary trait. It's in the same vein of design as Jax, Master Yi Lee Sin, Fiora, Vi and Xin Zhao. He's not an assassin, he's a fighter with assassin-esque qualities.
What are assassins' qualities, anyway?
-Focus on killing a single target at a time
-Prefer to fight squishy targets first
-Mobility to get in/out of fights
-Usually have some gimmick defense tool (stealth and untargetability are common)
-Often have CC
Huh, looks like Jax, Lee, Xin, Fiora, Vi, Yi and Yasuo do a lot of that. But, wait, what was the primary archetype? Oh yeah, they're Fighters.
Funny thing about Fighters, they're all designed as front-line champions, which means they need to be able to deal and take damage. This is because they don't deal significant burst damage; their strength is in high DPS instead. Instead of being the average assassin's 2-3k damage in 2 seconds, they deal a ton of damage as the fight extends.
No, Yasuo is not an assassin, when compared to Kha'zix, Fizz, Talon, Zed, Katarina, Leblanc, etc.