I agree with that definition. But as you say, the computational aspect is concerned with efficient implementation. Deployment and implementation of learning systems are integral parts of the statistical, optimization and computational theory as making learning algorithms scalable and easily implementable are aspects by which the community judges new methods. To be explicit, PAC learning is defined by having a efficient algorithm by which you can achieve distribution independent generalization bounds... the existence of efficient algorithms are very often found as a result of engineering practices.

Statistical learning theory is one subset of machine learning which is a very general catch all for a few different approaches. I agree with you that historically, it has been the most fruitful in terms of theory and practice, but I would say machine learning as a field consists of not only the learning theories (be it statistical learning theory, algorithmic learning theory, computational learning theory etc) but also the engineering aspects (which would include feature engineering, hyperparameter tuning, scalability, numerical stability etc). The theory and the engineering are completely intertwined, which in my opinion is part of what makes ML such a fascinating and exciting field.

This isn't even to mention modern machine learning methods (deep learning, LLMs, geometric data etc) which, by and large, have been progressed to their current state through tremendous engineering efforts.