old 230 volt transformer style arc welder on an old square d 125 amp panel
While the panel is rated 125 amp, you have a 100 amp service. You also have an electric dryer and water heater in addition to the usual lights and outlets. Adding a 66 amp load to all of this is definitely overloading the service.

If you went ahead and installed this welder, you won't burn down the house (at least not from electrical loads, from welding is another story) but you would get nuisance tripping. Every time you struck an arc, the lights would dim. The resulting voltage drop could damage electronic equipment such as computers and TVs, as well as anything else with electronics, which is virtually everything these days.