I agree with Tim's answer, but I'd like to add that you shouldn't think of it as changing chords. What you're doing (i.e. playing this on two strings) is actually correct and it's not like 'getting away' with something, but that's all that's to it. It's a line imposed over a chord: the chord is a dominant seventh chord (i.e. in a basic blues either the I7, IV7, or V7) and the line goes from the 5th of the chord to the 6th (and it sometimes moves on to the b7th). It happens quite often that the basic harmony is static while some line is moving. See also this answer for the more general concept of a moving line over a static chord.

I agree with Tim's answer, but I'd like to add that you shouldn't think of it as changing chords. What you're doing (i.e. playing this on two strings) is actually correct and it's not like 'getting away' with something, but that's all that's to it. It's a line imposed over a chord: the chord is a dominant seventh chord (i.e. in a basic blues either the I7, IV7, or V7) and the line goes from the 5th of the chord to the 6th (and it sometimes moves on to the b7th). It happens quite often that the basic harmony is static while some line is moving. See also this answer for the more general concept of a moving line over a static chord.