Tap with two fingers for a "right-click" or secondary click

There are 3 checkboxes in the top of the Preference pane you show as a screenshot. The third one, which you have unchecked, enables "tap to click" - turn this option on and you'll be set. If that one is off, you must click (rather than tap) for all other options shown.

I have a MBP 2018 with Mojave on it and I have that same dialog like this:

I find it easier to look at the trackpad options using the defaults command vs. navigating the dialogs that have become a confusing mess going from one version to another of macOS. On my system I have the settings like this:

$ defaults read com.apple.AppleMultitouchTrackpad
{
    ActuateDetents = 1;
    Clicking = 1;
    DragLock = 0;
    Dragging = 0;
    FirstClickThreshold = 1;
    ForceSuppressed = 0;
    SecondClickThreshold = 1;
    TrackpadCornerSecondaryClick = 0;
    TrackpadFiveFingerPinchGesture = 2;
    TrackpadFourFingerHorizSwipeGesture = 2;
    TrackpadFourFingerPinchGesture = 2;
    TrackpadFourFingerVertSwipeGesture = 2;
    TrackpadHandResting = 1;
    TrackpadHorizScroll = 1;
    TrackpadMomentumScroll = 1;
    TrackpadPinch = 1;
    TrackpadRightClick = 1;
    TrackpadRotate = 1;
    TrackpadScroll = 1;
    TrackpadThreeFingerDrag = 1;
    TrackpadThreeFingerHorizSwipeGesture = 0;
    TrackpadThreeFingerTapGesture = 0;
    TrackpadThreeFingerVertSwipeGesture = 0;
    TrackpadTwoFingerDoubleTapGesture = 1;
    TrackpadTwoFingerFromRightEdgeSwipeGesture = 3;
    USBMouseStopsTrackpad = 0;
    UserPreferences = 1;
    version = 12;
}

I'd compare your settings with mine to see what's amiss. If you find one of the settings is different you can use defaults to change it as well.

Example

Here I'm merely cycling the values for the property FirstClickThreshold to illustrate how one can use defaults to write and then read values.

$ defaults read com.apple.AppleMultitouchTrackpad | grep FirstClickThreshold
    FirstClickThreshold = 1;

$ defaults write com.apple.AppleMultitouchTrackpad FirstClickThreshold 0
$ defaults read com.apple.AppleMultitouchTrackpad | grep FirstClickThreshold
    FirstClickThreshold = 0;

$ defaults write com.apple.AppleMultitouchTrackpad FirstClickThreshold 1
$ defaults read com.apple.AppleMultitouchTrackpad | grep FirstClickThreshold
    FirstClickThreshold = 1;