From left to right on the main window:
Sidebar*: Swipe horizontal: Switch "All Items" / "Unread" / "Stared"
Article List*: Swipe horizontal: show / hide sidebar
Swipe horizontal: Switch "Article summary" / "Clutter-free" / "Website"
Note: In Website mode you can use horizontal swipe to navigate back/forward, the same way as you can do in Safari
Swipe vertical: next/previous article
You can disable/enable News Reader gestures at Preferences / General / News reader section
*: Three finger swipe gestures do not work. Make sure that “swipe between pages” option is not set to "swipe with three fingers” in System Preferences / Trackpad. If it is set to "two or three fingers" option, you can only use two finger swipe