Mortise and tenon joinery is good, but pocket screws with glue is also extremely strong.
Dowels, when used with actual wood (not press board) is also plenty for this application.
Looking at this design, the main issue is racking forces, which M/T joints may hold up slightly better to, but a thin sheet of 1/4" plywood stapled or glued on the back and sides would also lock this into place and prevent racking.
Really, this design is probably fine, but there's a handful of details that aren't shown, and would be critical to the success.
