Well, it's depends. There's a lot of variables at play. Wrestling and striking exists at two different ends of the strength-velocity spectrum to a large degree. Maximal strength will be more important in wrestling, but explosiveness and being able to generate strength at moderate velocities still superseed that, in most instances. As far as the specificity of strength in general, you're not entirely off base, but not entirely on it either (setting aside the fighting example).
Strength adaptions can be non-specific to an extent (tissue strength, fiber characteristics, tendon stiffness, maximum voluntary contractions, injury reduction) and
may transfer to other movements. You don't
have to use deadlifts, squats, single leg exercises, rows and presses to build this, however those exercises are a good way of practicing basic movement patterns. At the same time, strength adaptions are also specific, and in some cases highly specific (velocity, dynamic/static, joint angles, surface, stability requirements, contraction velocities, contraction type, energy systems, and neuromuscular control/motor learning). Usually the higher the skill, the more specific the adaptions, or at least you need a certain type of strength at the exact moment during a movement to benefit the most. Another example is when something is biomechanically similar. The squat and the vertical jump have somewhat similar mechanics, and improving squat strength has shown to be able to improve vertical jump height,
IF the weak point is maximum strength and not velocity (meaning it depends on the individual force-velocity profile).
Overall strength GPP seems to be benefical in reducing the risk of injury as well improving basic movement patterns and creating a foundation for building other attributes, like power, down the road. However, moving past that phase, either sport specific drills, or sport drills, are most likely more beneficial. The load ranges, velocities, exercise selection and so on depends on goal, I'd say.
I agree that compound movements require specific skill (more than some people give them credit for) that has just as much to do with practicing motor patterns and having the right leverages, as it does with maximum voluntary contractions (strength) of specific muscles.
She's a freak outlier for having that kind of upper body strength but there's lots of girls out there who can squat or deadlift over 400 and without even being that big. It's not that rare
She's such a specimen, it's quite amazing. Total freak, in a good way.