dave, take a look at figure 7 in the lm317 datasheet.
https://www.st.com/stonline/books/pdf/docs/2154.pdf the guy that designed that power supply used 4 resistors instead of 2. In the datasheet you will see one resistor between output and Adjust (R1) and one between adjust and ground (R2). the formula for the output voltage is Vout = 1.25(1+ R2/R1) +Iadj*R2. For small R2s, you can ignore the Iadj*R2. What he was trying to do is get specific values of R1 and R2 so he could get exactly 9V. I would suggest you get 1% metal film resistors. R1 = 120, R2 = 732 (those are stocked values of xicon 1% metal film at mouser). This will give you very close to 9V (at least 8.95 but with the Iadj adder, it's almost exactly 9V). edit: note that 750 will get you 9.14V and 720 will get you 8.8V)
so, remove all 4 resistors from the board. replace the 274 ohm one with 120. Replace the 6K81 one with 732.
Now, I don't understand why the guy didn't just use a 7809. no resistors needed at all, Unfortunately, the pin out is different from the LM317 so the board won't work.