The transformer can be omitted, if you find a suitable, cheaper one. Take a look at this questionthis question for more information about the exact requirements.
I don't think the other parts can be omitted, as...
- A motor clearly is required to motorize something (#88002)
- A motor won't work without a battery (#8878)
- Something motorized that can't be controlled is senseless (#8879 & #8884)
In addition, you could try to buy these 4 parts on Bricklink, which is a bit cheaper, so you end at ~$105 (+ ~$10 for a third party transformer) - this should save you $35 (~25%).