I don't entirely understand the system at play with the game. The randomized stage selection is at best un-fun and at worst broken. After 15 random rolls I only ever got Japan, Egypt, Rome and the boat. I don't even know what the other 3 stages look like, much less if I'm even suppose to get to them. The items are also confusing. They appear to have a chance to spawn each time you go to a stage, so is it intentional design to make the player spam random time travelling to stock up on items? Usually for a game like this you'd want to make a storefront for stuff like this. Beat an enemy, get a currency, use the currency to buy items for harder fights, etc. At least then the player would be incentivized to fight the enemies they randomly travel to.
Onto the combat itself. Limiting defense completely breaks the game, especially in conjunction with how SP works. Because you don't start with SP the game is just a 50/50 game, and if you have more Defense than the opponent then the only correct option is to just Defend until you run out to take away their defense and increase your multiplier. Your opponent will run out before you do, meaning that the game once again just becomes a 50/50 game. The fact is that you're never actually playing RPS. Technically if you both run out of Defense, you're just playing R, because why would either of you ever pick SP if there's no Defense to break? Even the SP tiebreaker is bad design because either you're good enough at mashing to never lose, or you're bad enough at mashing to never win. How is that a tie system? (Small note, even you seem aware of this given that instead of making the third character get something special on SP ties to match the others, you give them a weird power that has nothing to do with the battle mechanic.)
With that said, the game looks cute, the pixel style is alright and the music is decent without being too repetitive. It's an interesting prototype, but the game needs a firmer idea on what it's identity is suppose to be. Is the game suppose to capture the randomness of RPS or the strategy of the game? If randomness is the goal, ditch the permakill and make all three options have an infinite or semi-infinite amount of uses in a battle.(Also ditch this design where repeated fights in one stage make you start off weak. Every fight should have you at your best). If strategy is the goal, make SP do something from the beginning of the match, make the items and stages not random and instead bake patterns and characters into the individual stages so that when you beat the opponent you didn't just beat a random AI, but instead an opponent with something to dictate how they work.(i.e. animated or pose based tells for moves, taunts to inform what they're doing or a personality that hints at their play style). This will also allow you to drop overly high HP pools for enemies and cheap items like the Ankh that remove all skill from the battle.