TweetGuns here is my take on it.

So we know, muscles have to be stimulated and broken down to grow. Some anti oxidants reduce inflammation and reduce muscle growth slightly.

This may do that BUT... it can allow you to train harder, longer and more often while having less oxidants in your body. So your gains at worse would be about even either way. You might as well take it for your overall health feeling better and having less inflammation in your body.

Astaxanthin in Exercise Metabolism, Performance and Recovery: A Review.