Yes. Guy by the name of John Doan was or is the quintessential twin paradox (that time dilation actually works the way Einstein predicted) idiot on Usenet and the Internet for going on 50 years now. He in't even a crank; he's like a flat Earther or something. Did you know, Thomas Dolby was like the first member of the Flat Earth Society's? GREAT music talent, no doubt. Don't really know why either of them can't abide the idea of relativity. Don't care.
The acceleration of one twin with respect to the other has nothing to do with the different rates of aging of the twins. The asymmetry of one of the twins inhabiting a moving reference frame for an extended time interval with respect to the time the other twin spends in the "rest frame" they previously coexisted in is what accounts for the differences in their respective ages. Acceleration is simply how this asymmetrical state of motion is accomplished.
The trajectory of the twins with respect to each other doesn't matter. It works for a circular trajectory of any practical size as well as it does for a linear one. The closer to the speed of light one twin goes with respect to the frame of the stationary twin, the more time dilates and the more noticeable their age differences when the twins are reunited.
Time isn't just a complex number assigned to a 4D component of a spatial coordinate because it has an arrow with a direction we cannot move freely in. Time is literally 100% the real coordinate we refer to as 'space' for all three of those (or any of an infinite number of other) directions. ALL directions are proportional to time, but even that is only part of the puzzle. Unlike a single direction we designate as space conceived of as a snapshot of a single photon traversing from one end of the 3D Euclidean universe to the other, bulk matter literally owes its temporal permanence to energy components propagating as they rotate and are entangled with each other and with the quantum field in which they exist at a quantum level much faster than that. Only the centers of particles of matter experience time at a rate that is at rest with respect to a beam of light propagating at c or with particles belonging to another twin still at rest. The rest frame is defined by +/- c, and by the zero QUANTUM SPIN AND ENTANGLEMENTS of the Higgs field, and without an understanding these are essential coupled descriptions of physical motion unrelated to a snapshot of a Euclidean universe conceived by a bias of a solid geometry that is anything but solid.
You are EVERY ONE OF YOU like John Doan. Just as much an idiot as he was/is. You should all join the Flat (or else the non-spinning) Earth Society. Physics doesn't work very well when you neglect rotation and relativity as it applies to energy and time just so you can do Ancient Greek geometry in a coordinate system with the wrong origin. Time is more relativistic than it ever was Euclidean, and space does not exist any more than a flat Earth does, other than where you are standing right now, grasshopper.
Ponder THAT for a while, martillo.