why are there only resistors hence the output varies between + and -
Can't understand this.
The circuit has a virtual ground at mid-rail (2.5V) generated by the two 10k resistors
and decoupling capacitor.
The CT output is measured relative to this so it varies above and below 2.5V across
the mains current cycle. The Arduino ADC cannot tolerate negative voltages so
you have to offset the input like this.
Have they forgotten something?
No, they know what they are doing of course, many eyes and all that.
Another thing I'm not getting is the type of the CT. They said the CT used in the guide is a current output type but the datasheet doesn't say anything about current. As seen in the datasheet, only U=f(I) charts are shown.