The tailgate should self center unless there is dirt or other debris in the pivot points.
In this photo, it's easy to see one problem that is contributing to the misalignment. The top corners of the the tailgate are higher on the left and lower on the right, causing the gap to close up tighter on the right. There may also be some damage to the bed sides or the tailgate itself but that's hard to tell from the picture. (Accident?)
It looks like the pivot mounts on the bedsides may have been damaged or misadjusted at some point. I don't know if the pivot mounts are adjustable - I've never tried to adjust them. On my truck, it looks like they might be.
To remove the tailgate, support the weight of the gate and depress the retainer spring clips to release the two cables. Then raise the gate to its halfway position - about 45 degrees. You can then slide its pivot out of the right hand mount and then out of the left. This can be awkward to do alone and it's safer for the tailgate if you have help.