In the official Thread some one linked TES Legends Twitch stream, when they mentioned what counts.
https://forums.elderscrollsonline.com/en/discussion/482283/official-discussion-thread-for-ride-your-free-doom-wolf-mount-into-the-elder-scrolls-online#latest

deadsheepb14_ESO wrote: »

https://www.twitch.tv/videos/445524917##

00:33:00 is where he explains you just need to win 3 games.

So apparently "ANY " 3 wins will count. I mean they THEY said so it should count I guess.

SgtSilock wrote: »

Story games aren’t recorded though, wouldn’t it need to be in your match history for it to count at least?

Maybe, But if you go to your in-game profile, there you have your overall statistics. One of those is "Games Won". So I do believe this is what you need to do.

But tbh. I played the tutorial, then the whole story campaign, and after that I was like "ok, what do I do next ?"

So I played some "Casual Play" mode (vs other player)... and... I actually managed to win some of them.
Well... I am a total noob but I do believe that the story mode is there so you could learn "basic's basic".

I am actually glad we have this promotion in ESO as because of it I discovered that TES: Legends is actually pretty good game.