A Score Reel is fitted with a printed circuit board when the game needs to know what digit is showing on the score reel. All score reels have switches to stop them at zero when resetting, and most have another switch to carry to the next higher digit when showing a nine (e.g. 90 -> 100). If the game needs any more information than that, a printed circuit board and wipers are added to identify specific digits. In your case the 10s digit is probably used by the match circuit to award a free game, so the game needs to know which digit is showing when deciding whether or not you matched at the end of the game. The 1000s and 10,000s score reels are probably used by the replay score circuitry, to award a free game when you pass whatever score thresholds are set.

The 100s digit doesn't have a circuit board because the game never needs to know if the 100s digit is showing anything between 1 and 8.

The buzzing may be due to the coil being loose in its frame, or perhaps a loose or damaged coil stop. Coils in score reels often have a thin, potato chip shaped spring washer between the coil and the frame, around the coil sleeve, to keep the coil under tension and keep it from vibrating. I'd compare the noisy coil to a quieter coil and see if you can identify any mechanical differences in how they're mounted or how much wiggle room they have.

/Mark