Just keep it
To the very least, for consistency sake. But also think about this: what if the user has a broken volume control on his/her device? You'd be providing an experience where user has lost the locus of control, which is one of the main things to avoid when designing your UX. The more control, the better, the less control, the worse. Do not worry about some small redundancy, since it won't affect your usability in a negative way. But NOT HAVING that control may cause real problems.
Additionally, some people likes to use on screen controls (me being one of them) whenever possible. For example, I leave my iPad on a stand and control volume with the on screen controls. Having to search for the physical controls would be extremely uncomfortable, would make the iPad fall or move from its position, would add additional work on a control when it's not needed at all. So, as you can see, there are lots of advantages on keeping it and, quite probably, not a single disadvantage.
Finally, sites like Soundcloud or YouTube use volume controls, and believe me they have tested things extensively with much more resources than what you have, so take advantage of that knowledge and use it on your site
EDIT: Added screenshots
Here you have Soundcloud on Safari / iPad and YouTube on Chrome / Android, you can clearly see the volume controls. Also, it seem you're confusing a responsive site with an adaptive version or even an app. Keep in mind not only they're not the same, but each one has its particularities. But even then, you should never take control off from the user