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There’s really not a single “the G chord” as there are various G chords. In this case the strums are just brushing the treble strings and hinting at the chord, which is ok because you just picked that nice deep G base note on the low E string. Now technically a chord is three notes and a G major is G B and D. As charted there’s no B in that. If you want a B, using a 3 finger G chord and leaving the b string open is certainly an option. Of course, you are free to catch the B on the A string on the strums. That would work fine on the down strum. Going too far into the base on an up-strum feels weird. Usually you only catch a few of the treble strings.
As for direction, there’s nothing on that chart to indicate direction. There’s a convention that usually for 8th notes, on the beat is down and the “and”s are up. But that’s not etched in stone. Sometimes when it’s important and not obvious you little Vs for the up strokes and little staple like marks for the down strokes.