You can create catalog price rules that are triggered by a particular product attribute or by a particular attribute set, but no, out of the box you can't trigger rules against product type itself.
For this particular case it may be as simple as applying a price rule to Guy's shirts category itself - but that will also catch non-configurable products in that category.
To do this more specifically, you could add one or more extra attributes to your products that you use for targeting. So you could create a dropdown attribute called "Price Rule Group" and populate that drop down with a list of tags that make sense for your store, you can then target the catalog price rule against those tags.
One thing to watch out for, when creating the new attribute/attributes remember to set "Use for promo rule conditions" to "Yes" or the attribute won't show in the price rule conditions list.
The disadvantage of this method is that you're creating a new attribute to replicate data that is essentially already there in your case. However the advantage is that you can be more flexible, so if you had a Women's blouse in a different category that was only a simple product - but that you wanted to share the price rule, now you can.
This approach doesn't work as hoped for on variant products as not all variant attributes are passed up to the checkout code and I suspect I missed that when I first read the question.
If you have this issue then one work around is to use the variant price to target the rule. As the variant price becomes a cart item attribute it is available to the promotions code.
So this way you can apply a rule based on an attribute of the configurable product, but that then only applies to a variant with a specific cart item price.
Of course this only helps if your variants have different prices!