CheckNew3DS is called in two functions. This is only used for disabling UI button(s) for downloading New3DS titles when running on Old3DS. For example, on a New3DS patching a CheckNew3DS func-call with <retval=0>, results in the download button on the app page being grayed-out for a New3DS-only title.
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==TitleID checks==
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There's titleID checks in the system eShop application code for "Pokémon Omega Ruby". This appears to be used with UI-related code, unknown why.