The EasyGift product picker used to select trigger and action products for a given rule shows the available products on your store. By default, the product picker filters out any products which are not set to active, these states include:
Some apps (like Recharge) create duplicates of a given product to create the subscription version which exists to not be made available on the online store.
If you want to use these types of products on an EasyGift rule then please contact support. We can make the product picker display these products by changing a setting on your account.