>>This isn't exclusive to SLRs.
No, it is not, but, for a given price point, you will likely get faster AF with an SLR today than all but the most expensive mirrorless cameras. Especially with motion tracking. I know that there are some cameras that say they'll be faster, but having tested a bunch in the real world, I had a very hard time finding any that worked as well as SLRs in as wide a range of conditions.
>>This is more about sensor size than whether the camera has a mechanical mirror box inside.
Yes, though it is more complex than this. It also has to do with the distance from the sensor to the back of the lens. This doesn't require a mirror, but most mirrorless cameras are focused on reducing the size of the package, so they try to reduce this distance so they can shrink their lenses. This is not an absolute advantage of the SLR, but the form factor currently lends itself to this characteristic, while mirrorless bodies are typically trying to optimize for something else. (of course, many mirrorless cameras can use adaptors to full-frame SLR lenses, and the results can be great image quality, but typically bad performance on autofocus.)
source: Spent several days with A7R, A7R2, Canon 6D, 5D3, 5DSr. Tested lenses Canon 11-24, 40mm, 24-70ii, 70-200, sony 70-200. Ultimately bought the 5DSr, due to more reliable functioning, ergonomics, lenses, battery life, etc. Despite genuinely wanting to shed the weight.