They are compatible. Your question was 'does the PSU have the necessary PCIE connectors to run the graphics card' and I said yes it has two PCIE power connectors, the card needs one.
Usually a 550W is enough for a 1070 and yours is 620W. Is it a new PSU or you've had it for long?
I provided the link to the Asus specs page to make sure you meant that exact card.