Yes, I do know what 60 fps means.

This video was captured with the shittiest capture card and, as you can see, it's 60 fps. If you advance frame by frame, you'll see the game timer advance every frame and, of course, it takes 60 frames for it to count a full second.

So, like I said, if the capture card mentioned by the OP is compliant with NTSC (which I'm guessing it is, even my shitty card is), then it will allow for 60fps to be captured. And, finally, what I'm trying to say is that you don't need Dolphin, HDMI shenanigans or expensive capture cards in order to get 60 fps, but you do need them for good quality.

20xx TE will make it so that you only need Dolphin tho, which is amazing!

EDIT: Here's another video (that wasn't upscaled so I can't upload to youtube, since 720p unlocks 60 fps), that was captured with an even shittier card -- this one, similar to the one Kadano linked down in the comments -- and I still got 60fps. Please do ignore my less-than-sober mumbling throughout the video.