I thought I'd follow up on this... finally.
After reading the comment about having the termite guy drilling into the drain pipe, i popped the clean out cap to discover that there is a 90 degree elbow about 12 inches under the surface which puts the drain pipe about 8 inches from the house slab... so even if the termite guy drilled that far down he'd still miss the drain pipe. I also did confirm that the pipe indeed has shifted and broken about a quarter inch just under the bottom driveway.
The pipe pic I originally posted shows one of two drain pipes... that attached photo shows that there are actually two... the closer one being for the washer, the farther one for the kitchen sink. What wasn't making any sense was why I got no leakage when using the sink but got leakage using the water.
Then, one Saturday afternoon, I was washing a couple of paint rollers, 2 or 3 paint brushes and other assorted equipment, using a fair quantity of water, when all of a sudden, paint laden water started coming out of the washer drain... the one with the break.
Then the light bulb came on. The drain had to be clogged somewhere. This particular line is dedicated to just the sink and washer. It runs about 70 feet across my yard, where it is coupled to a 4 inch pipe that drops at a 45 degree angle to connect with a sewer pipe that is 16 ft underground. I had this put in years ago because the trees in my yard completely broke up the existing concrete pipe chunks.
In any event, I had a cleanout installed just in front of the connection to the 4 inch pipe. Sure enough, using a snake cleared a blockage. Once the blockage was gone I've had no additional water from the break in the pipe.