Would Yi unstoppable with wiki master legend and 16 XP get stunned and prevented from moving by Vex Apathetic that is at a battlefield?

Yes, Master Yi, Unstoppable (even at Level 16 with the "can't be chosen" protection) will still be stunned and prevented from moving by Vex, Apathetic.

Reasoning

This interaction is covered by RiftJudge FAQ #9545:

• Programmatic Selection vs. Targeting: Master Yi, Unstoppable's Level 16 ability states: "I can't be chosen by enemy spells and abilities." However, Vex, Apathetic’s ability does not require the opponent to manually "choose" or "target" a unit. It uses programmatic selection, meaning the ability automatically identifies the unit that triggered the condition ("When an opponent plays a unit").
• Protection Bypass: Protection from being "chosen" only applies to effects that require a player to manually select a target. Because Vex’s ability automatically identifies the unit based on the game event (you playing a unit), it bypasses Master Yi's protection.

Sequence of Events

1. You play Master Yi, Unstoppable.
2. Vex, Apathetic's triggered ability activates because you played a unit while Vex is at a battlefield.
3. The ability programmatically selects Master Yi.
4. Because the unit is programmatically selected rather than chosen, Master Yi's protection does not apply.
5. Master Yi becomes Stunned and gains the restriction that he cannot move for the remainder of the turn.