How do I provide a “show all posts” link in a paginated term archive?

This method will set it up so that if you add /all to the end of your taxonomy archives, it will show all posts.

First, when registering the taxonomy, make sure you set the ep_mask to EP_CATEGORIES. This means we can add a custom endpoint to it.

function wpse_277843_register_taxonomy() {
    register_taxonomy( 'game_go_series', 'game_go', array(
        'rewrite' => array(
            'slug'    => 'series',
            'ep_mask' => EP_CATEGORIES,
        ),
    ) );
}
add_action( 'init', 'wpse_277843_register_taxonomy' );

Don’t copy all that code, just make sure you do the ep_mask thing in your code, because it’s probably not already set that way.

To add ep_mask to Custom Post Types UI generated taxonomies, do this:

function wpse_277843_cptui_ep_mask( $args, $taxonomy_slug, $taxonomy_args ) {
    if ( 'game_go_series' == $taxonomy_slug ) {
        $args['rewrite']['ep_mask'] = EP_CATEGORIES;
    }

    return $args;
}
add_filter( 'cptui_pre_register_taxonomy', 'wpse_277843_cptui_ep_mask', 10, 3 );

Then create the all rewrite endpoint to the EP_CATEGORIES mask.

function wpse_277843_all_endpoint() {
    add_rewrite_endpoint( 'all', EP_CATEGORIES );
}
add_action( 'init', 'wpse_277843_all_endpoint' );

This does mean that the endpoint will also be valid for Categories, but we can ignore them for any custom behaviour later. Unfortunately adding endpoints only to a custom taxonomy appears to be impossible right now. It just means that going to /category/category-name/all won’t throw a 404. The /all will just be ignored (or you can apply the same behaviour for categories, if you want).

Then, in pre_get_posts, if the all endpoint is accessed on your custom taxonomy, set posts_per_page to -1:

function wpse_277843_all_posts( $query ) {
    if ( $query->is_main_query() && $query->is_tax( 'game_go_series' ) ) {
        if ( isset( $query->query_vars['all'] ) ) {
            $query->set( 'posts_per_page', -1 );
        }
    }
}
add_action( 'pre_get_posts', 'wpse_277843_all_posts' );

Then you can add a link to your template to the /all version, if you’re on a taxonomy archive already, and if it’s not already the /all version:

<?php if ( is_tax( 'game_go_series' ) && get_query_var( 'all', false ) === false ) : ?>
    <a href="https://wordpress.stackexchange.com/questions/277843/<?php echo get_term_link( get_queried_object() ); ?>all/">
        Show All
    </a>
<?php endif; ?>