The Linus Roadster is not the bike I'd choose for rural poor quality tarmac, gravel roads or packed dirt trails.
The stock 32mm tires do give a bit more volume than standard road size tires to soak up bumps a little (they are about the the same size as cyclo-cross tires ) but they are slicks designed for paved roads. The main problems are the single speed drivetrain and rear wheel only coaster brake. (There's also the fact that the bike screams _urban hipster!!!_ )
You don't need a full-on mountain bike for poor quality tarmac, gravel roads or packed dirt trails as long as they are relatively smooth without big bumps and holes. If you want flat bars a hybrid would work well. You don't need a suspension fork and tires 35-40mm wide with a medium tread pattern will be fine. If you want drop bars gravel bikes are ideal for these sorts or surfaces as well.