It would need customization to implement this menu dropdown, Unfortunately, there is no simple solution otherwise I will be happy to help you.
I would suggest hiring a Shopify expert to assist you OR feel free to contact me.
You can use the following app for the dropdown.
Thanks for your question, As you know every theme is different and so are their html structure.
To change the menu item views to look like the other one it required to change the html structure.
You can change it in your thems navingation file or get a help from a developer.