A video player is web tool. It could be designed to have an appearance that would remind of the certain brand and by having the options to be embedded and shared it could help generate links and thus contribute to the SEO efforts. I see it as a web content development, quality content or link bait. What do you think?
So having a customized video player is nice for site appearance, given the content is relevant to your site and people might link to it based on quality, then yes it can't hurt and could help improve the site's overall traffic. I wouldn't spend tons getting someone to do this who is trying to sell you on something.
If the video is embedded properly and satisfies the search engine principles , then there is also chance of having good positions in the search engine results pages.