Does Ezreal legend ability still trigger if the spell is countered?

Yes, your Ezreal legend ability can still be activated if the spells you played were countered.

According to RiftJudge FAQ #9631 and RiftJudge FAQ #10536, the requirement for Ezreal's legend ability is satisfied the moment you choose the targets for your spells and finalize them on the chain. Because the act of choosing targets occurs when the spell is played (and finalized on the chain), the condition for the legend ability is met at that time, regardless of whether the spell subsequently resolves or is cleared from the chain by a counter effect.

The Sequence

1. Playing the Spell: You play a spell and choose target(s). This choice is locked in as the spell finalizes on the chain. This satisfies the "chosen" condition for Ezreal.
2. Reacting: Your opponent plays a counter (such as Defy) to counter your spell.
3. Resolution: The counter resolves, and your spell is cleared from the chain per Rule 425.1.a.
4. Activation: Because you have already completed the "choosing" action, you may now exhaust your Ezreal legend to activate its ability and draw a card, provided you are in an Open State (the chain is empty and you have focus).

Note: While a countered card is not considered to have been "played" for effects that require successful resolution (like "When you play a spell" triggers for cards such as Virtuoso), the act of "choosing/targeting" required by Ezreal's legend ability is completed as soon as the spell is finalized on the chain.