Very ambitious, very creative!
I understand the mechanic of only being able to damage the opponent in each one's pocket-dimension, but it's kinda lame when both dimensions are the exact same, and all 3 dimensions are not really tailored to the game's physics. There are a lot of floating platforms that you just don't interact with at all, and the pocket dimensions are the exact same layout for both players. I would think the dimensions would give the owning player an advantage... The main dimension is just an open hallway, essentially. I understand if you figured there being no cover would help the game start off faster, but it runs the risk of instead being not very engaging, especially since you can't hurt each other until you enter a respective pocket dimension...which, with an open hallway, you don't really have reason to approach, lest you risk getting portal'd yourself.
Now, I do like the idea of needing to trap the player into your dimension to hurt them and the initial dimension being a "neutral zone". But, the map design should be thought over again. And I think there should be a way back to the initial map to essentially reset the game to neutral if the opposing player can avoid being killed for long enough. Perhaps revisit some of these ideas and lean into the competitive states if you continue development.
Overall, this game is pretty cool! I see the vision: it could use some work, but either way I'm still impressed!