The stroke of the valve is twice the offset of the hole in the centre of the eccentric.
I think it's meant to be 3/16" stroke, it's just dimensioned badly. 3/8" would be way too much.
This means the central hole in the eccentric needs to be 3/32" off centre, as illustrated. This means the outer edge of the 0.120" hole is at just under 5/32" from the centre, leaving 1/16" of metal which is plenty in my book.
This will only mean the valve opens by 1/32" at each end of its stroke, but I don't think that will be a problem. The critical dimension is the 1/8" at the end of the valve and ensuring that is lined up with the inlet passage at (valve) mid-stroke.
I think the 3/32" dimension is a radius for a decorative recess on the eccentric, leaving a rim 1/32" wide. This has no purpose and other wise the engine is very functional, but you can make out such a tiny rim on the drawing.
Neil