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?
If you put great content on your website it will increase your traffic due to relevance for what you have and what people may be searching for. A player with no videos is just a browser….so it really matters how you TAG your videos and how you embed this player in your page in a way that the crawlers can identify what the content of this page is so that they know how to categorize it into their search results.
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.