An "S" trap goes down, then goes up, then goes down again before reaching a vent within the required distances. (i.e., a 1.5" "P" trap with an 8 foot horizontal span is still an "S" trap, just not as obvious as the "S" traps you can buy at Lowes.)

Nuffin' wrong with the P-trap, except...

It could possibly be a crown vent, if the distance from the trap to the vent is less than twice the pipe diameter. But that's hard to tell from the photo.

So, if there's a vent in the wall not too far away, but at least 2.5" away for a 1.25" trap, or 3" away for a 1.5" trap, that configuration is fine.