I installed gamepress and nextgen on a test wordpress install I have.
It works, so that rules out the theme.
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A bit of digging in the code and it looks like this is a roles/permissions issue.
Are you the only user of your wordpress install, and you installed it yourself?
If you go to the NextGen roles section, it allows you to select the lowest role that is allowed to do which action.
Go to wordpress Users->All Users menu. Check what you role is (there are 5). If your the only one, you should be admin.
Then, go to NextGen Gallery->Roles. Since you probably want to be able to access everything make sure all the settings are at your role, or lower (if you want to give other people access).
The order is this, from most capability to least:
Admin
Editor
Author
Contributor
Subscriber
If you have other users, figure out who should have access and set everything up accordingly.
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If that doesn’t work, it may be a bug in another plugin or the wordpress install, affecting user roles…
I want you to test something. Make sure your logged in as admin and nextgen is installed.
Go to this address, replacing the bit with your web address:
https://*YOUR WP URL*/wp-admin/admin.php?page=nextgen-gallery
Make sure, if wp is installed in a subdirectory, to include that too.