the frame itself may be twisted, too... check for alignment between the wheels... remove the tires from the rims, then align the front wheel with the rear wheel, VISUALLY, by looking along the front rim's sidewall, then the rear rim's sidewalls... if there is any deviation seen, then you've found the issue... if not, then disconnect the shifter cable, and take a test ride...

i have also visually checked for frame twist by looking down the head tube, and comparing it's alignment to the seat tube... but that can be difficult to detect, unless 'you have tape measures in your eyes"... i've been accused of that... ;-)

that bike has been down lots of roads... no telling what may have happened to it... the single shift cable may be the issue.... SIS Stranded-type cable housings are notoriously stiff..... swapping for a coiled steel type cable housing may eliminate that problem, if your test ride shows no pulling to one side....

just looked at the pics again... noticed BOTH cables that run to the rear of the bike ARE ON THE SAME SIDE... This will cause the problem! the front brake cable will not load the steering, the other two WILL load the steering! Switch the BRAKE CABLES around... see what happens!