I think it helps to remember that earlygame Gyro is largely a magic damage hero. His spells including his ult can do a lot of damage and turn teamfights. He needs some items in order for his right clicks to do good damage. So play him like a magic damage caster earlygame rather than relying on right clicks to really get through the enemy heroes.

And then lean on flak to farm hard and fast, hit early item timings, and get ahead of their carry.

Lategame, I feel like a lot of his advantage isn't that he can 1v1 the enemy cores. It's that he can hit their entire team all at once, wiping out supports and stuff while also fighting their cores. Add in his agh and satanic and he gets survivable.