Material Design According to Google, drawer menu's (or navigation drawers) don't require a close button. Interaction with the
content still visible on the right or by pressing a link in the menu
will close it.
iOS Apple doesn't have any official guidelines on drawer menu's.
Pushing content aside This is a popular interaction you can see a lot on Dribbble. The drawer menu pushes the content right. The
hamburger icon moves with it. Interaction with the button or the still
visible content will close the drawer. No close button is displayed.
So, a close button is not necessary perse, it's optional.
But if you do want to add a close button, where to put it?
Mac vs Windows A great way of deciding where to place elements is to think about where your users would expect it taking in account
any other conventions. Problem with this is that you can seperate
people on this subject into windows users and mac users. Windows users
would expect it in the top right corner. Mac users are used to it
being on the left hand. Although the Windows group is larger, it is
not a safe to assume the right side would be the best.
So you can't really fall back on solid conventions, what can you do?
I think keeping it as close to real world physics as possible is the answer. You do this by keeping context with animations and simulating real behaviour.
If your navigation drawer slides over the content from the left, I would put the close button in the top right corner. When closing a real drawer you push on the outer end, not close to the closet. Also, the animation draws the eye from the left to the right.
Pushing content all the way to the right
If your navigation drawer pushes the content all the way to the right I would put the close button in the top right corner for the same reason I mentioned above.
However, if your content is still partially visible I would strongly recommend considering not using a close button at all.
Fading layer on top
If your navigation fades full screen on top I would place the close button on the same spot the hamburger button was.
Looking at your design I see both hamburger icon and close icon. What does the hamburger icon do at this point? So answering your question if that is right: no, not in combination with the hamburger icon still visible.
Hope this helps.