If he continued moving inertially, then what he measures in his frame (which is different from what he see
--look at this thread
if the distinction isn't clear to you) is just as valid as what is measured in any other frame. But as long as you stick to a single inertial frame for the entire problem you'll conclude the traveling twin ages less in total (the laws of physics work the same in every inertial frame, but they don't work the same way in non-inertial frames). For example, you could take the perspective of the frame where the traveling twin was at rest during the first phase of the journey while the Earth is flying away, and in this frame, he will age more than the Earth prior to the turnaround, but after the turnaround he'll be moving at an even greater
speed than the Earth, and so be aging slower. It'll work out that when you add how much he ages in both the outbound stage and the inbound stage, and compare it to how much the Earth ages from start to end, the traveling twin still ages less, by exactly the same amount as if you had used the rest frame of the Earth.