Yes they need to be updated. The little arrows point to magnetic north from the station's location thus indicating the variation. As MN moves, charts need to be reprinted.
Heading compass / gyro is magnetic, the complete navigation reference system is magnetic, VORs need to be magnetic too in order to fit to the system. It would be overly complicated to apply correction for NavAid variation in practical use.
Same reason why the ATC reported wind is also magnetic - provided for practical an immediate use. Unlike METARs and TAFs, which for practical reasons need to be geographic.
cheers, FD.