That map hasn't got Newton Abbott to Moreton Hampstead via Heathfield and it branch via Chudleigh to Exeter closed 1958. The branch to Princetown is also missing.
The railways killed the villages of central Devon.
The map says 'Services under consideration for closure in August 1962, which in some cases have already been withdrawn, are included in the map" but it does not back to all lines ever open. So missing from the map that I notice (in addition to yours) are:
* Totnes to Ashburton
* Fowey to St Blazey
* Barnstaple to Lynmouth
* Bridgwater to Edington
* Plymouth to Yealmpton
* Bideford to Appledore
* Yatton to Blagdon
* Highbidge to Burnham