The very fact that the exact opposite is also true validates bigger maps are more strategic. Take a super super tiny map and the strategic options are clearly very limited. I've played with many chessmasters and any of them will clearly tell you the number of strategic choices would greatly increase if an additional 64 squares are added in between the players of a chessboard as would the strategic options decrease if any squares are removed from the default game board. It's mathematics, if necessary keep making the tiny map smaller until you recognize the difference.
Comparing a game like Elemental to Chess is a bad analogy. Chess has a small subset of simple rules, on a small board and you can do just one thing on each turn. I would agree with you if we were talking about tactical combat in games like HoMM, but not about something like the whole game in totality. There are so many things you can do in a game like Elemental that are so far beyond the scope of Chess that you'd need to use the Hubble Space Telescope to see it. You can recruit units, use magic, engage in diplomacy... In chess, the number of pieces on the board hardly changes; as the number of pieces dwindle, so do the options. In games like Elemental, the reverse is usually true.
For absurdly small maps where there isn't room to move, sure. But once you pass a critical size, everything blooms to infinity in the absence of a time limit. And with a time limit, the number of permutations of things you could do would be unimaginably large. So large it would look like the number chess games look like an infinitesimal fraction. But as far as I know there will be no time limit, so there is absolutely no upper limit on the number of ways to play a given game. Technically this also applies for absurdly small maps, too!
And even in the presence of time limits... Saying "there are more strategic options in a giant map because you can play 10^643 different ways, whereas you can only play 10^452 ways on a small map" is absurd in the extreme, because no one would ever notice. As long as the smallest number is large enough that a person can't even imagine the vast majority of potential decisions, then adding more is not going to make the game any more strategic.