Magento2: Overriding the catalog widget

You have to just rename your theme module directory like Magento_CatalogWidget.

New file path for your theme: mytheme/Magento_CatalogWidget/templates/product/widget/content/grid.phtml

When core module name with - you have to remove that and make the next character Uppercase.

Eg.: if you want to override core module module-catalog-inventory then your path would be Magento_CatalogInventory.