http://www.pinwiki.com/wiki/index.php?title=Williams_System_3_-_7#Segment_failures
"Players 3 & 4 Segments
BCD inputs are A2 B2 C2 D2 from the MPU board
MC14543 BCD to 7-Seg. Decoder IC8
UDN7180 Display Driver IC10
Resistors R8-R14"
page 15 in the .pdf manual shows the burnt resistor is R11 part number 58-8981, FC, 10 K OHM 10% 1/2 W. That falls in the range Pinwiki lists as potential problems so I think you're on the right track.