Welding current isn't a problem, like, if there were an obvious path through low current wires, they'd have melted and burned up long ago. You'd barely be able to strike an arc before noticing the problem. Or be able to hold an arc once the traces/wires fuse...
It's the sparking that's a problem, and also HF start if applicable. The voltage drop along a rigid metal beam can be massive when it's done very quickly, and the time frame can be as short as single nanoseconds, for fast sparks through air. HF start typically consists of microsecond bursts, at high energy (some ~mJ doesn't sound like much energy in general, but in such a short time frame, it's a lot of peak power!), which can in turn be sharpened by sparking action to the nanosecond scale.
And even if the structure is grounded (it certainly should be -- in the very literal sense, being buried in post holes!), and the welder is grounded (through power cable or otherwise), these are all pathways with substantial length -- grounding doesn't exist at high frequencies, these are only galvanic (mains / DC) paths. They might as well be open circuit, at high enough frequency.
But on the flip side, these should all be environmental stresses the controls are built to handle. Cables routed through air are subject to ESD where people may be in contact, and induced lightning when subject to nearby strikes; buried cables are additionally subject to lightning ground-return surge. (Which might not be a big deal; the control cables can be insulated inside of whatever box they terminate in, no need to make a ground loop; it does need to be insulated well enough not to spark under those conditions.)
Not that most of these are very frequent -- they might simply not design for nearby lightning strikes. And like, direct strike might seem promising (consider a gate at the edge of a flat field!), but is just too immensely destructive to bother trying to protect (~100kA surge!).
(There's also mains surge, which is typically induced or direct lightning strike, conducted on the mains distribution network -- which is not as destructive because there are surge arrestors and transformers between the strike and most any customers. It's also isolated from the control by its power supply. So this seems an unlikely route to be affected by welding.)
So, it could be poor design, but there's still possibility it's due to unexpected paths. And like xavier mentioned, maybe something went through (or didn't) the bearings/guides, maybe the designers made a faulty assumption about those being good grounds so didn't bother putting protection on some connections across them, etc.
Tim