As I thought, that looks to be a proprietary design. You will almost certainly either be stuck with the power supply you have or limited to getting one from MSI that uses the same connector type, which is not an obviously standard design from what I can tell.
It also looks like that's likely only about a 140w unit, which is absolutely not likely to be enough for a GTX 1060 that needs about 130w more than your 1050 TI. I'd contact MSI to find out if they offer a higher capacity model that is suitable for use with your system. Otherwise, unless somebody else knows better and has an inside scoop on that particular unit, I think you are probably stuck with what you have.