Without discussing the competitive scene, and without discussing tournament presence or the lasting impact of Dominion on League of Legends play, I'd like to take a few moments and discuss the perception that Dominion won't be "as strategic" as Summoner's Rift, because it's a harmful misconception that will foster a lot of annoying elitism if left in place.
People who hold to the idea that Dominion will be "more casual" often offer three key points of evidence. I'll address both in turn:
1. "Riot has stated that Dominion was designed to be more appealing to casual players."
This is, to put it plainly, a straw-man argument. In the interview which those who hold this opinion typically cite, Zileas says that the game will be accessible to casual players, not just hardcore LoL fans. This says nothing about the level of strategic depth the mode offers. Of course they're going to say that Dominion is accessible to newbies. Riot is debuting a brand-new game mode, with a shiny new map, and that sort of news, following headlines that highlight LoL's enormous player base, is the kind of news likely to attract new players. Irrespective of the depth of strategy that the game mode eventually offers, Riot doesn't want to alienate a single potential player. Why would they? Portraying your company as being only for hardcore fans gains you nothing. Riot is both a business and a collection of artists, and both professions only benefit from bringing in new blood: every noob is a potential hardcore fan later on.
And anyway, Dominion WILL be more accessible, but not for the reasons most people imagine, and certainly not due to a lack of depth. "Capture and hold" game modes have been present in first-person shooters for years now, so many gamers will be familiar with the concept; that alone is enough to make it more accessible.
2. "Games are short compared to Summoner's Rift; there will be less time for strategic maneuvering."
I cannot at all see why shorter games would lead necessarily to less strategy, and I know a thing or two about short-burst strategy: before I came to League of Legends, my main video game genre was fighters, in which a full match will almost always take less than five minutes to complete. Fighting games are not less strategic for their short duration; in fact, I'd say that the speed makes fighters more strategic, because poor positioning becomes infinitely less forgiving. Consider a game of Dominion for a moment: in Summoner's Rift, a moderately lost teamfight might mean that the opponent gets a dragon, or pushes up to a tower. There's time to recover from that. But in a game mode where every minute counts far more than it would otherwise, there's less time to recover: a moderately lost teamfight in Dominion might mean that Heimer and Shaco get to set up nests and hold a capture point so imperviously for the next five minutes that your team is put irreversibly behind. That might be a bit of an exaggeration, but in a shorter game mode, it follows logically not that there will be less time for strategy, but that careful strategy will be of far more importance.
3. "This isn't what a MOBA looks like. It won't be strategic like a MOBA is supposed to be."
Of course it won't be. If you say this, you are absolutely on the money. But that doesn't make it less strategic. In fact, it's my favorite part: In Dominion, with the focus placed squarely on the champions and their slick, varied abilities, gameplay will be less about coordinated flanking and more about knowing how to cooperate as a team, who on your team combines best together, etc. That, to me, is very cool.
TL;DR: Try before you judge. Dominion will be very strategic.