Yes you need to purchase the jw player to get rid of the watermark. You could ask this question specifically in the Joomlaworks forum forum.joomlaworks.net/ You might be able to get a logo free version by joining them.
In the past it did not have the logo. If you can find an old copy with out the logo, some people have reported success replacing the new copy with an older version that didn't have the logo. I couldn't tell you where to find one though.
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