If one takes the reflexive order relation as fundamental, which is a good practice since in the context of pre-orders, one can define the strict order $<$ from the reflexive order $\leq$, but not necessarily conversely, since there are strict orders $<$ that arise from more than one pre-order, then this is just the product order.
That is, if one understands an "order" to be the reflexive relation, which comes along with its defined strict relation, then one has the (reflexive) product order relation, and your relation is the strict order arising from that product order.
So one could call this the (strict) product order, understanding "order" to be the reflexive relation, which comes along with its derived strict order.
But as you note, it is not the product of the strict orders, and I view this as one more reason that we don't want the strict orders to be primary.