The badge will be applied on all the new products (less than 7 days). To add it to a specific product, you have to create a category apply a badge on it and add this category to your product.
Or you can create a custom field in the table product, and add a check for the badge display, like:
if((($this->row->product_sale_start == 0 && $this->row->product_created >= time()-604800) || $this->row->product_sale_start >= time()-604800) || $this->row->yourfield == 'show_badge'){
$this->classbadge->placeBadges($this->image, $this->row->badges, -10, 0);
}
In this case, the badge will be displayed on the products published less than 7 days, or on the products with a value of "show_badge" for the custom field named "yourfield".
You can change the code to display the badge only on the recent products having the custom field value.