See Vehtari, Gelman and Gabry (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. In Statistics and Computing, 27(5):1413–1432. doi:10.1007/s11222-016-9696-4. Preprint

Yes, but only if 1) you don’t get high k values from Pareto-k diagnostic from loo() function, 2) the model is well specified, 3) no outliers, and n is large (at least in hundreds). If you get high k values, then waic is biased, and if the model is badly misspecified, there are outliers or n is small, then the interval is not well calibrated (although it may still contain some useful information)

Suppose that four conditions you mentioned above are satisfied and two CI are non-over lapping. The first WAIC and its CI is 73693 [72775, 74611] and the second is 114921 [113935, 115908].

In this case, is this safe to say that the first model is better than the second?

Please note that I had run two models and I only saved the output as an excel file containing WAIC and its SE, so I cannot use function compare or similar function in LOO package.

For log densities, higher value is better. So you need to also clarify whether above values are based on log densities or negative log densities (and maybe even further multiplied by 2) , The difference in performance is clear.