The "metagame" describes the competitive/race aspect of testing and discovering new strategies from match to matches, adjusting for changes to rules and the strategies you see others employing. I'd say it's this change over time across many individual matches and rulesets that justifies the "meta" part of the term to differentiate with adjustments you might make or try to make within one match.

The term "meta" is often colloquially used to describe a currently dominant strategy... in other words, whatever's winning the metagame. "Meme-game" could be a less flattering but also pretty accurate description of how "the meta" often plays out with a kind of herd mentality.

It doesn't mean strategy. It's basically the strategy of the strategy (or the game of the game, hence the term Meta). It's about finding the new strategy before your opponent. It becomes a game unto itself.

MetaGame is not strategy. The metagame is often the behind-the-scene variables that enable a certain set of strategies to flourish.

For example, in Dota, changes to armor or magic resistance scaling can change the metagame to be magic or physical focused, but the strategies and trends themselves develop in ways that take the meta-game into account.

During one meta game, it is common to see various different strategies flourish. IMO, as it is one level of abstraction higher, it is fair to call it meta-strategy and by extension the meta-game.