You are using permitted routes in three sets of circumstances:
1) If you are on a direct Maghull-Manchester train, of which there are none,
2) If you are travelling by the shortest route, which is certainly not via Chester,
3) If you are travelling on a route defined in the National Routeing Guide:
http://www.atoc.org/about-atoc/rail-settlement-plan/routeing-guide
Maghull is a related station to the Liverpool Group, Preston and the Wigan Group.
http://www.atoc.org/clientfiles/File/routeing_point_identifier.pdf page 39
We now need to find which of these routeing points are appropriate by comparing fares:
Maghull-Manchester Stns:
SDS £11.90
CDS £11.00
Liverpool Stns-Manchester Stns:
SDS £11.90
CDS £11.00
Both fares the same as the Maghull fares, so Liverpool is an appropriate routeing point.
Preston-Manchester Stns:
SDS £10.60
Cheaper than the Maghull fare, so Preston is an appropriate routeing point.
Wigan-Manchester Stns
No comparable fares, the SDS and CDS have a destination of Manchester CTLZ.
All four Manchester Stations are members of the Manchester Group
http://www.atoc.org/clientfiles/File/routeing_point_identifier.pdf pages 18 and 40
Routeing Permissions for Liverpool Group-Manchester Group are: LY, ML and PS.
http://www.atoc.org/clientfiles/File/permitted_route_identifier.pdf page 596
LY allows:
Liverpool-Earlstown-Manchester
http://www.atoc.org/clientfiles/File/Maps.pdf page 70
ML allows:
Liverpool-Huyton-Wigan-Bolton-Manchester
Liverpool-Huyton-Wigan-Atherton-Manchester
Liverpool-Huyton-Earlstown-Newton le Willows-Manchester
http://www.atoc.org/clientfiles/File/Maps.pdf page 74
PS allows:
Liverpool-Earlstown-Manchester
Liverpool-Hunts Cross-Warrington-Manchester
http://www.atoc.org/clientfiles/File/Maps.pdf page 91
The only routeing permission for Preston-Manchester is: NW.
http://www.atoc.org/clientfiles/File/permitted_route_identifier.pdf page 786
This allows:
Preston-Bolton-Manchester
Preston-Wigan-Bolton-Manchester
http://www.atoc.org/clientfiles/File/Maps.pdf page 85
Therefore, I conclude that your ticket is not valid via Chester.