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The answer is in your documentation link under Common Mistakes:

Wrong folder path – Files within the templates folder are not put
within
wp-content/themes/twentyten/plugins/events-manager/templates/templates/, note the extra templates folder in this path compared to the previous
one.

Use /plugins/events-manager/templates/ instead. I.e. you need to copy files inside the plugin’s templates folder to your theme, not that first templates folder.

The plugin should then fetch these files automatically.

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