Building defensive items increases your damage output. It just doesn't increase your DPS.
The more sustained the nature of the damage you deal, the more defensive items increase your damage output, by letting you stay in the fight longer.
That's the whole nature of building Warwick and TriForce+tanky items. You survive in order to get the proc once every two seconds, every two seconds.
It's also why I dislike the pure dps calculators which suggest something like 4 IE and Blackcleaver, or some such.
You have "Damage intervals".
Opponent deals 500 damage every 0.4 seconds. You have 2,000 life. That's constant.
Case A: You deal 1,000 damage every 0.9 seconds. DPS: 1,111
Case B: You deal 400 damage every 0.5 seconds. DPS: 800
In both cases you die after 1.6 seconds, but whereas in case A you deal 1k damage, in case B you deal a total of 1.2k damage before dying.
Some things are counter-intuitive, DPS is one of them, since you don't deal damage at the end of the second simultaneously to the opposition, and you need to survive in order to output damage.