It's probably one of the highest quality emulators out there. For example it is fully compatible with the Gamecube and Wii controllers using your computer's Bluetooth. They've reached a level where the console can even access the Wii Online community and appears to Nintendo's servers as a legitimate Wii (you still need to grab the encrytped blobs from your console though).
To all intents and purposes they've completely emulated a Gamecube and Wii and then gone many steps further in improving audio and graphics (original Wii is capped at 480p - Dolphin can go to 4K or beyond with visuals rivalling even the new Nintendo switch).
I'm not interested on the ps2 so I don't know about the current status of its emulation, but this is what neobrain(author and contributor of a lot of emulators) thinks about its management: https://www.reddit.com/r/emulation/comments/2ttbdk/play_the_...
Another reason dolphin blog reports are so important is because they inform the community about progress and why decisions were made, that makes it looks more friendly, open and democratic
To all intents and purposes they've completely emulated a Gamecube and Wii and then gone many steps further in improving audio and graphics (original Wii is capped at 480p - Dolphin can go to 4K or beyond with visuals rivalling even the new Nintendo switch).