I wouldn’t expect that recipe to lead to a light, fluffy cake. Gingerbread is often quite dense and I that’s what I would expect here upon initial reading.
The only acid is the milk and treacle to balance the bicarb. Next time, either, add a little cream of tarter or take out the bicarbonate entirely and use sr flour. A little vanilla essence might be a worthwhile addition.
Or, you can separate the eggs, stir in the yolks, whisk the whites until stiff and fold in last thing.