No, Hori sticks AND Mad Catz stock joysticks should have 8-way movement.
What people are feeling is a SQUARE gate. It may be square but you can definitely do diagonals and roll motions. Many people recommend square gates because most inputs are equidistant. That’s not true for other gate styles.
These gates are restrictors that keep joystick movement within measured bounds and also keep Japanese-style joysticks from literally shaking themselves to pieces!
The other gate styles are octagonal, circle/circular, four-way, and 2-way. The stock gates that come with Sanwa and Seimitsu joysticks can be popped off (Sanwa) or unscrewed to allow a new gate to be positioned and screwed onto the joystick (all Seimitsu joysticks I’m aware of).
Octagonal and circular are 360-degrees like the square gate and the second-preferred style of gates for fighting games. Some people like these better because they can’t get used to rolling motions on Square Gates. I like these alternate gate styles on the Sanwa JLF, myself, because I have a hard time with the square gate on that stick. On the other hand, I find it easier to use square gates on the Seimitsu LS-32-01 joystick and am more consistent with it. Everyone has their preferences…
As for four-way gates, it’s what it means. Movement is restricted to Up and Down, Left and Right. This is good for old-style arcade games like Pac-Man and Donkey Kong but horrible for fighters for obvious reasons.
Two-way gates obviously restrict joystick movement to either Up and Down, OR Left or Right. Only movements are vertically or horizontally. They’re good for classic 2-D shooters like Space Invaders (right-left) or for engine throttle movement (up-down).
The only reason why you’d install a 2- or 4-way restrictor gate on a joystick is if you’re a retro-gamer. With an 8-way restrictor gate, you can easily input diagonal directions that can get you killed in those games. 2- and 4-way restrict movement so that you’re more precise with old-style classic arcade games from the late 1970s and early 1980s.
P.S. – While it’s easy to swap restrictor gates on JLF and Seimitsu joysticks, the stock joysticks on both the Hori and Mad Catz beginner bases are NOT designed for swapping.
You can technically retrofit the stock joysticks with about any restrictor, but it’s an involved mod job especially for Hori sticks which have built-in square gates… Those square gates are part of the joystick housing! You’ll be cutting some plastic there for sure.
I am not so sure about the Mad Catz stock joysticks for the SE. I have a Wii Tatsunoko Vs Capcom joystick which as an identical base housing BUT its buttons and joystick cloned from the Sanwa buttons and JLF joystick! The tolerance on my original Wii joysticks (which I took apart to recycle for usable pieces) were so tight that it was unfeasible to put a JLF octo-gate on it even though it was cloned after the JLF! I took that joystick and installed a JLF. That Mad Catz stick was junk!
Can’t say for sure about the MC SE joystick. I’ve heard they’re garbage, too, but they were made to be replaceable with arcade parts at any rate. I’m sure people have managed to fit Sanwa restrictors on those, too.