No, it's not linear in input voltage. It means that the LEDs have the threshold voltages specified in the datsheet:
View attachment 138309
If you want a linear characteristic, use LM3914 with uniform threshold steps.
Consider that moving-coil S-meters have also linear scale. So even if the receiver characteristic isn't really linear, it's a better estimation than the LM3915 log curve. Although an S-meter is showing field strength in a log scale, the log characteristic is already achieved by the AGC transfer function.