It means the user must check to see whether there are any legal obligations other than those mentioned in the rest of the contract. So the agreement will list various obligations relating to the use of the product but this doesnt mean that there aren't any other obligations which need to be complied with - it is up to the user to ensure compliance with any obligations not mentioned in the contract.
Basically the contract is saying "we dont know what all the obligations are and it is up to the user to check whether any more exist or not". It is putting the onus of complying with any obligations (whether in the contract or not) on the user.
"do not exist" means something isnt real - you exist, your house exists, China exists, The Loch Ness Monster does not exist - it is not real. If there are some other obligations somewhere then they exist, if there are no other obligaions then they do not exist.
Contracts are typically difficult to understand, even for English speakers, because they are worded so as to be interpreted as widely as possible.