It basically means 'does not have'
She has no 눈치 because she "put it in rice and ate it"(metaphorically, of course) while everyone else knows it's something to keep on the outside and use wisely.
'말다' is a way of enjoying food in which you pick up a serving of rice and put it in 국 (국 is a type of Korean food which has liquid and solid half and half).
A normal and peaceful example sentence would be 국에 밥을 말아서 먹다.
So, why would you say 눈치를 밥 말아먹다 instead of just 눈치가 없다? It's because you're that stressed just having a thought of her 눈치 없음. You can't help letting some of the stress out by saying something twisted like this.
A sister expression is '쌈 싸먹다' (It could also be 눈치를 쌈 싸먹은 은하라도).