Hello Arachyd

,
Here is the reason why it might risk a person's account if he play on multiple devices with different ip addresses :-
I think, with changing your computer, you also mean to change your ip and I hope you also know that if any of the account is found to be accessed via multiple ip addresses then Splitscreen would think that the account is being shared unless mentioned otherwise by you via a support ticket. After Splitscreen notices multiple addresses of an account, the account could be marked as an "Account shared between multiple users" and the penalty for it is an indefinite suspension of that game account.
However, a person can minimize this risk by sending a ticket to the support (which costs only few minutes of time to write and explain about the problem to the team).
{c} Transfer / Trading of Accounts and Account Sharing
The transfer or trading of accounts is strictly prohibited; all game accounts represent virtual property of Splitscreen Studios GmbH and their affiliates. This includes any form of account sharing, which is defined as the use of a single account by one or more additional players that are not directly associated with the account.
You may check out the complete rules and regulations for playing any game owned by Splitscreen Studios GmbH over
Here.
I hope this helps, Please do rectify me if I am wrong anywhere.
Best Regards,
Pr0Ankit