You have the correct intake. The quote is BS. I've been running the Mazdaspeed CAI for over three years. It is a rebranded AEM. The issue is not with the Gen 1 -- its Gen 2, which does uses a different diameter MAF housing. If you have Gen 1, then this is an excellent intake, in either Mazdaspeed label or AEM. Make sure you do have the air straightener in your kit. Some early releases from Mazda did not have the straightener, and it is important.
Here is the AEM instruction pdf. I think it's pretty clear and no video should be necessary. Make sure you install the air straightener and align it correctly.
I've also attached Mazda's instructions and its separate paper on the straightener and a copy of the Mazdaspeed recommendation for alignment or "clocking" of the straightener. Please note that Mazda and AEM are not in agreement on clocking position. Mazda thinks it matters, so I use the Mazda recommended position. This clocks the dot on the outside rim of the straightener pointing at the middle of the MAF sensor. This positions the vanes of the straightener at about a 30 degree angle to the right of the MAF sensor when looking down the inside of the tube.
I hope this helps.
NOTE: AEM does not provide instructions, it seems, for installation of the splash shield. But I think it is important. It is covered in the attached Mazda instructions. It's simply held on with two supplied bolts that go into the bracket on the end of the CAI right above where your filter attaches. Don't worry about the spash shield being bigger than your filter. It's intended to fit up closely to that left front fender liner when the liner is put back in place.