After a bit of a mix-up, the official Overwatch twitter account confirmed that Competitive Play, which was stripped from both the open beta and the full release after its short run in the closed beta, will be implemented in June.
Seems the tweets have been deleted now, as I've been unable to find them, even following links from other websites. For now, it seems GameSpot is the only one with solid evidence this happened. Other sites' links only lead to error pages. Hmm... What could this mean...?
For now, I'll believe they still want to roll out Competitive mode in June, but I'll be sure to tread cautiously until we hear more from Blizzard and not the twitter account. I hope nobody got in trouble for those tweets...