If all you had pressed was LEFT, current would be #$02. The procedure repeatedly reads 4016, shoves the value bit into carry (the LSR command), then rotates it into current. Since 8 reads occur, current contains an entirely new value when it is completed. Since LEFT is the seventh item read, it is the seventh bit shifted in, and since it's shifting in from right to left (ROL), it ends up in the #$02 place.

The routine I quoted actually is designed to work with a battery of other routines and constants, which allow you to check if a direction or button is down, up, has just been pressed, or has just been released. (That's what the 'last' variable is for - for comparisons to detect falling and rising edges.) Also, it defines bitmasks so you can check to see if DOWN and A are active, say, by the code:

    ldx #$00   ; Controller 1
    lda #input'dir'down | input'btn'a
    jsr input'down
    bne _not'pressed
    ; Code for dealing with DOWN+A here
_not'pressed:
    ; Code continues