"By 'abstract labor' Marx means work done simply in order to earn a wage, rather than for the worker's own specific purposes. Thus making a pair of shoes because one wants a pair of shoes is not abstract labor; making a pair of shoes because that happens to be a way of getting money is."
"Marx: A Very Short Introduction"
By Peter Singer
Pg. 33
I think that the example is probably correct (this probably is abstract labour) but misleading (it does not explain why it is abstract labour). This example would be better to illustrate alienated labour. Abstract labour is labour when thought of independently of the labourer's individual being, but as the thing which can produce value. Perhaps an example would be: "I have 100 tree trunks. I want to turn them into planks. I need to hire labour to operate the machines that do this." Here I am talking about abstract labour. It's got nothing to do with any individual, or how they experience the work. To realise my need for abstract labour, I go out into the labour market and buy the best value (i.e. cheapest per output) labour power (comodified labour) I can.
So all in all, and without knowing the context, I think the description misses the point a little. It's more about the alienation of labour than the abstraction of labour. Though you can't really have the one without the other, but both concepts, whilst co-dependent, are distinguishable.
(p.s. my marxist jargon ain't perfect, so can others please correct me if I'm wrong. Also, Singer is a eugenicist dick, but let's not open that can of worms)