If you don't want to use the word to cover the things it usually covers, then I'd suggest using a different word, or adding some qualifiers.
Why say, "A distinguishing feature of modern design philosophy is to design with intent*" and confuse people, when you could say, "A distinguishing feature of modern design philosophy is to design with a clear, narrow focus and mechanics that drive play in pursuit of that focus."
The former might be briefer, but it's also essentially wrong, especially if you leave out the footnote. There is no need to redefine a word to be used in an arbitrarily limiting way when there are better ways of expressing the point and, if you are going to use this special, limited definition which is not an established or understood piece of jargon, it is certainly your responsibility (assuming you wish to communicate clearly) to make your special, limited definition clear before you start using it.
So, sure, I agree that designing with intent* is a feature of modern design philosophy, but it is absolutely untrue that modern design philosophy has any special claim to designing with intent.
*"intent" here means only the intent to have a a clear, narrow focus and mechanics that drive play in pursuit of that focus, and not other types of intent as the word is commonly understood.