Great start! I have a number of things to mention here as a veteran game tester.
I dig the original idea being a fusion of RPS+TTT but it needs a bunch of animations. People go nuts over animations, so they're extremely important, such as the graphic actually moving when using the Move card (with acceleration and deceleration, too, not just at a fixed speed), and kicking out the old one (make the beaten graphic rotate and fall off or fade or something).
Make the game include its own built-in tips so you don't need a tutorial: put a check box in the settings to optionally show or hide guidance text that is always there, such as "Tap a card," "Tap an empty space to summon the card's monster," "Pick a monster," and "Move the monster to an empty space" (with a glowing and fading selection border to indicate which monster you've picked; there is currently no indicator for monster selection).
Don't score the TTT condition right away; I was first confused by how the enemy just immediately landed a point with everything on the board vanishing. Have it first draw a line explaining how they won, animate a victory point that then flies to the corresponding side's point bar, and then smoothly dissolve-or-whatever-you'd-like the board's creatures; never just show or remove elements with no animation, ever! This is what makes games appealing as much as their mechanics.
There are more things for me to mention such as the upper-left gear icon getting slightly cut off on my Galaxy S23's screen. If you're open to a joint endeavor, I'd also be interested in potentially supplying sound and music if I can find time.
Also consider "Rock Paper Scissors Lizard Spock" from the popular TV show The Big Bang Theory, though that would probably require a 5x5 board!
Also add the ability to hold and drag a card to a cell. I thought I was supposed to do that at first and got confused until I realized you must tap a card and then tap a space. Many games involving cards and their targets allow both options, like in Slay the Spire, Monster Train, etc.