The motion was granted with prejudice. Plaintiff failed to prove its case. Plaintiff cannot re-file. If timely, the plaintiff may make a motion for new trial upon the grounds specified in C.C.P. section 657.
You are technically correct that most authorities opine that a motion for non-suit is unavailable in a court trial. The correct procedure would be a motion for judgment.
However, IMO, if the ruling was correct the court will disregard its name – especially if the incorrect name was not called to the court’s attention prior to the ruling. Technical defects are nearly always ignored unless prejudice results.
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The court can entertain such a motion. Even if it was called a motion for non-suit, the court has the discretion to consider as a different type of motion that would have the same effect.