By the traditional translation of if/then sentences to classical logic, it is. If you want to go further down the rabbit hole, several things are debatable here: When people use if/then sentences, do they really mean material implication, where (A -> B) is equivalent to (~A OR B)? Also, people often use the word "or" in a sense that's closer to exclusive OR, as opposed to the inclusive OR that the logical operator indicates. Overall, can the meaning of a sentence with imperative intent be fully captured by a proposition that is just meant to indicate a state of affairs?

"Do finish the house chores" is more naturally taken as a command, so the question is whether it should be assigned a truth value at all. It is linked to some normative claims that would plausibly be truth-valued: "you are permitted to play Minecraft only if you finish the chores", or perhaps "you ought to finish the chores, or you are not permitted to play Minecraft". The former is equivalent to the original sentence only if we take "can't" as expressing lack of permission (which it may not): "if you don't finish house chores, you can't/are not permitted to play Minecraft".

And “If you don’t play Minecraft, you don’t have to finish house chores.”

"xor you can't play Minecraft" is correct :)

you sure?

I think "if you don't you can't" does not preclude other don'ts leading to you can'ts, but "Do or you can't" means that if you Do you can, although in normal vernacular usage you are right that they are interchangeable.