You could use DragGesture

.gesture(DragGesture(minimumDistance: 0, coordinateSpace: .local)
                    .onEnded({ value in
                        if value.translation.width < 0 {
                            // left
                        }

                        if value.translation.width > 0 {
                            // right
                        }
                        if value.translation.height < 0 {
                            // up
                        }

                        if value.translation.height > 0 {
                            // down
                        }
                    }))

With the other solutions being a bit inconsistent on a physical device, I decided to come up with another one that seems to be much more consistent across different screen sizes as there are no hardcoded values except for the minimumDistance.

.gesture(DragGesture(minimumDistance: 20, coordinateSpace: .global)
            .onEnded { value in
                let horizontalAmount = value.translation.width
                let verticalAmount = value.translation.height
                
                if abs(horizontalAmount) > abs(verticalAmount) {
                    print(horizontalAmount < 0 ? "left swipe" : "right swipe")
                } else {
                    print(verticalAmount < 0 ? "up swipe" : "down swipe")
                }
            })

If you want one that is more "forgiving" to the directionality of the swipe, you can use a few more conditionals to help even it out:

EDIT: did some more testing, apparently the values for the second conditional add some confusion, so I adjusted them to remove said confusion and make the gesture bulletproof (drags to the corners will now come up with "no clue" instead of one of the gestures)...

let detectDirectionalDrags = DragGesture(minimumDistance: 3.0, coordinateSpace: .local)
.onEnded { value in
    print(value.translation)
    
    if value.translation.width < 0 && value.translation.height > -30 && value.translation.height < 30 {
        print("left swipe")
    }
    else if value.translation.width > 0 && value.translation.height > -30 && value.translation.height < 30 {
        print("right swipe")
    }
    else if value.translation.height < 0 && value.translation.width < 100 && value.translation.width > -100 {
        print("up swipe")
    }
    else if value.translation.height > 0 && value.translation.width < 100 && value.translation.width > -100 {
        print("down swipe")
    }
    else {
        print("no clue")
    }

Based on Benjamin's answer this is a swiftier way to handle the cases

.gesture(DragGesture(minimumDistance: 3.0, coordinateSpace: .local)
    .onEnded { value in
        print(value.translation)
        switch(value.translation.width, value.translation.height) {
            case (...0, -30...30):  print("left swipe")
            case (0..., -30...30):  print("right swipe")
            case (-100...100, ...0):  print("up swipe")
            case (-100...100, 0...):  print("down swipe")
            default:  print("no clue")
        }
    }
)

I would create a modifier for simplicity. Usage will look like that:

yourView
        .onSwiped(.down) {
            // Action for down swipe
        }

OR

yourView
        .onSwiped { direction in 
            // React to detected swipe direction
        }

You can also use trigger parameter in order to configure receiving updates: continuously or only when the gesture ends.

Here's the full code:

struct SwipeModifier: ViewModifier {
    enum Directions: Int {
        case up, down, left, right
    }

    enum Trigger {
        case onChanged, onEnded
    }

    var trigger: Trigger
    var handler: ((Directions) -> Void)?

    func body(content: Content) -> some View {
        content.gesture(
            DragGesture(
                minimumDistance: 24,
                coordinateSpace: .local
            )
            .onChanged {
                if trigger == .onChanged {
                    handle($0)
                }
            }.onEnded {
                if trigger == .onEnded {
                    handle($0)
                }
            }
        )
    }

    private func handle(_ value: _ChangedGesture<DragGesture>.Value) {
        let hDelta = value.translation.width
        let vDelta = value.translation.height

        if abs(hDelta) > abs(vDelta) {
            handler?(hDelta < 0 ? .left : .right)
        } else {
            handler?(vDelta < 0 ? .up : .down)
        }
    }
}

extension View {
    func onSwiped(
        trigger: SwipeModifier.Trigger = .onChanged,
        action: @escaping (SwipeModifier.Directions) -> Void
    ) -> some View {
        let swipeModifier = SwipeModifier(trigger: trigger) {
            action($0)
        }
        return self.modifier(swipeModifier)
    }
    func onSwiped(
        _ direction: SwipeModifier.Directions,
        trigger: SwipeModifier.Trigger = .onChanged,
        action: @escaping () -> Void
    ) -> some View {
        let swipeModifier = SwipeModifier(trigger: trigger) {
            if direction == $0 {
                action()
            }
        }
        return self.modifier(swipeModifier)
    }
}

This is much more responsive:

.gesture(DragGesture(minimumDistance: 3.0, coordinateSpace: .local)
            .onEnded { value in
                let direction = atan2(value.translation.width, value.translation.height)
                switch direction {
                case (-Double.pi/4..<Double.pi/4): self.playMove(.down)
                case (Double.pi/4..<Double.pi*3/4): self.playMove(.right)
                case (Double.pi*3/4...Double.pi), (-Double.pi..<(-Double.pi*3/4)):
                    self.playMove(.up)
                case (-Double.pi*3/4..<(-Double.pi/4)): self.playMove(.left)
                default: 
                    print("unknown)")
                }
            }