You're right, it's both. So can we play/narrate like it's both?
If you like strategy, then find a way to make things story-oriented while also making them game-like. An equal balance. That should take some strategizing, and some creativity.
“…Judge not what a man has done, but judge what he could have done if he was a different bloke altogether. For art thou a leper? And a leper can changeth his spots…” --Rudy Wade, Misfits (Series 4, Episode 8)