The i7 isn't overkill for multi-threaded applications like video and music/graphics production and editing. It has Hyper Threading, which effectively doubles the number of cores available to the OS. The CPU in this box is roughly equivalent to the Haswell 4670K in terms of clock and IPC. This would be a sensible choice for a dual-purpose rig.
However, the i7 is overkill for Dolphin because it will not use those extra cores. Additionally, this will not play the most demanding tier of games at top performance because the Turbo Boost only goes to 3.9 GHz and it won't be possible to overclock this CPU with that SFF case. It wouldn't be easy anyway because I doubt that CPU is unlocked or the board has the ability to change those settings. That extra 300-400 MHz doesn't sound like much, but it's the extra bit needed to make some games run at full speed.
Still a good choice if you're willing to spend the extra money and have another purpose in mind.
However, the i7 is overkill for Dolphin because it will not use those extra cores. Additionally, this will not play the most demanding tier of games at top performance because the Turbo Boost only goes to 3.9 GHz and it won't be possible to overclock this CPU with that SFF case. It wouldn't be easy anyway because I doubt that CPU is unlocked or the board has the ability to change those settings. That extra 300-400 MHz doesn't sound like much, but it's the extra bit needed to make some games run at full speed.
Still a good choice if you're willing to spend the extra money and have another purpose in mind.