I have quite a bit of experience with Japanese cuisine. Due to my heritage I eat it and cook it quite a lot, and modify family recipes to primal quite easily, without sacrificing authenticity.
I would say:
Soy sauce = okay, as it is from fermented soybean. Make sure it doesn't have wheat added, as many Japanese soy sauces do. Best would be to probably go with wheat free tamari (made from whole fermented soybeans) or even Bragg's Aminos, or if you worry about soybean in general, try coconut aminos (flavour may be similar).
Sake: made from rice so not strictly primal/paleo, but two tbsp is way within the 80/20 limit and quite small when compared to the large amount of meat.
Mirin: same, however - this may be a bit bad, as lots of Japanese mirin have added sugar, or glucose syrup, or even high fructose corn syrup. Basically the idea is a sweet cooking wine made from rice - so made typically same way as sake, but with sweetener. I would say, probably avoid if you can, or substitute with primal sweet - like honey - if you really feel the dash of sweetness is important to the recipe.
Chicken powder: just make sure it is good chicken powder (if it exists)! Oftentimes, chicken broth and other broth powders have some of the most horrifying ingredients (fillers, hydrogenated oils, hydrolysed proteins) and are complete frankenfoods just used to give flavour. I'd say best is to use chicken stock and just reduce it, or if you can find a chicken broth powder that is not full of fillers and additives and fairly clean, go with that.
My word of advice though - don't necessarily go for the ingredients in the Asian market (with the Japanese labels) just for the sake of authenticity. I find very authentic taste can easily be re-created using more primal, clean, and reliable ingredients from American stores such as food co-ops, Whole Foods, Trader Joes... again, the most important is what the product is made of, and LOTS of commercial 'authentic' Japanese products are made with junk, frankenfoods, false flavourings and colourings and aspartame, preservatives, and crappy oils. My primal/healthy replacements for the 'authentic Japanese grocery products' have been homemade ghee mayo (for Kyupi mayo), wheat-free tamari (for soya sauce), sake (from Whole foods), homemade pickled vegetables (for umeboshi, ginger, etc), honey + sake for mirin, and lots of seaweed and miso which frankly, tastes and feels exactly the same as the Japanese store versions, but typically with better ingredients/more reliable sources.