There are multiple cases which aren't automatically dismissed due to this loss, including the defamation claim against Hodlonaut and the case over open source developers owing wright a fiduciary duty to author, publish, and (somehow) enforce a back door to recover billions of dollars worth of coins he says he lost the keys to.
As far as appeals go, determinations of fact are generally not appealable unless there was a clear error. Permission to appeal would have to be sought and aren't automatic.
If the judgement and remedies aren't forceful enough in this case, Wright may just begin the same litigation from another jurisdiction. On the stand he basically said that if he loses he will begin litigation on patent infringement grounds-- it isn't like having a baseless position has ever stopped him before.
To some extent it depends more on his funders willingness to keep financing him than anything else... he's given every sign that so long as he's funded and not incarcerated he'll keep it up.