Might work up north. Down here, in Texas, the termites would just look at that as an all-you-can-eat buffet!
I don't doubt it but wondered how all those Adobe structures with wood beams survived over the years?
Just wait until they discover the big holes in the walls when the wood rots out and insects attack it. Bet a hurricane would force water through the wood, too.
wet wood will swell with tremendous force, and break out that mortar. This is a short time design. They would do better to simply form it and pour a 3-4" wall in place. it would leave more room, could be foam insulated, and inner surfaces can be finished in any fashion desired,
...or go to their homepage and see where one of their walls has cracked between logs...not what they were trying to impress, I'm fairly certain.
Further west, drier climate, less friendly to termites, I would imagine. More than 1/2 of Texas is wet enough that you need to keep on top of termite infestation, or they'll eat you out of house & home.....literally! When I lived in Guam, I saw firsthand how the termites would chew through the outside creosoted layer of a wooden telephone pole (probably spitting that nasty stuff out behind them), then eat out the center of the pole, where the creosote hadn't soaked through. Hollowed those poles out like a drinking straw! Not even pressure treated lumber would withstand their appetites. If you build with wood there, and expect it to last, you use Philippine mahogany.....super-hard, super-dense! (like some politicians we know! LOL)