Many Shopify themes already support "Microdata" markup that provides the same sort of information that the JSON-LD for SEO application does – things like product information, prices, etc. You can check to see what sort of information your theme is currently providing to search engines like Google by testing your product URLs with Google’s Structured Data Testing tool.
The advantage of JSON-LD for SEO is that it will not only provide the same sort of information, but additional info about your store that allows Google to include your store in the Google Knowledge Graph. That allows for functionality like providing a Sitelinks Searchbox in Google results or displaying a company Knowledge Graph Card in search results.
Providing info via JSON-LD also means that the information about your products is separate from the theme you choose. This means you have less to worry about with changes to your theme, and also that as new JSON-LD features come out, your store’s markup can be upgraded automatically.
Ultimately, if your store already has Microdata markup, you may not see any huge benefits from the app right now. On the other hand, having both JSON-LD and regular markup on your store doesn’t cause any problems and does mean that Google may choose to offer those extra features like site search and information boxes to potential customers.