What brand PSU ? That is either a very old PSU or a crappy one. You can tell by the massive 3.3V output and the relatively small 12V output. The 12V output is mainly what modern PC components use, and that is 25A at 12V = roughly 300W. CPU and video are all 12v.
Any good brand 600W unit can run that CPU and that card in it's sleep. A $40 600W unit will typically not do so well. Your PSU, if it is a decent one, can still handle the load (your PC as below uses maybe 300W of mostly 12V, your PSU provides 300W), however if your PSU is crappy it will give bad noise and ripple at that load which might be OK or might cause intermittent BSOD type problems.
Your CPU actual power used is less than the rated 84W
The gtx 1070 is rated at 150W, might go higher OC'd
The rest of your PC (MB, Memory, disks) is less than 50W.
So it would be surprising to see that PC pull more than 300W. (400W at the wall before PSU efficiency). 600W is fine for that PC.
Update: for comparison, my 450 watt seasonic midrange G PSU label says 444W of 12V, more than the label spec on your 600W PSU.