common and literary usage.

120 princes were to report to 3 presidents, and Daniel was the lead president over the other two presidents. Daniel's conduct was so exemplary that these other rulers wanted to get rid of him. At this point, you should be aware that the book that you are working from is adding in the idea that the others felt shabby/mean/contemptible in comparison. I presume they are adding in this idea to explain that the other rulers wanted to get rid of him because of the way he made them feel bad and, perhaps, that they were jealous of him. However, since Daniel was beyond the corruption and bribe taking that many officials in any time period indulge in, it could be that he simply stood in the way of their running things the way they wanted and/or making bigger profits.

Anyway, since his behavior was beyond reproach, they decided the way to get rid of him was to show him as disloyal when given a choice between the law of God and the law of the land.


References:

shabby
Etymology: obsolete English shab a low fellow
Date: 1669
1 : clothed with worn or seedy garments <a shabby hobo>
2 a : threadbare and faded from wear <a shabby sofa> b : ill-kept : dilapidated <a shabby neighborhood>
3 a : mean, despicable, contemptible <must feel shabby…because of his compromises — Nat Hentoff> b : ungenerous, unfair <laments the shabby way in which this country often treated a poet — Paul Engle> c : inferior in quality <shabby reasoning>
http://www.merriam-webster.com/dictionary/shabby

Daniel’s behavior distinguished himself above all the other rulers. Daniel was beyond corruption, with any new government and new positions, corruption and bribe taking would be in the offing. Daniel more then likely would not play the game, his uprightness and righteousness would cause problems [for those who were] bent on reaping huge profits in a new government.
http://www.truthnet.org/Daniel/Chapter6/

mean – adjective, -er, -est.
1. offensive, selfish, or unaccommodating; nasty; malicious: a mean remark; He gets mean when he doesn't get his way.
2. small-minded or ignoble: mean motives.
3. penurious, stingy, or miserly: a person who is mean about money.
4. inferior in grade, quality, or character: no mean reward.
5. low in status, rank, or dignity: mean servitors.
6. of little importance or consequence: mean little details.
7. unimposing or shabby: a mean abode.
8. small, humiliated, or ashamed: You should feel mean for being so stingy.
9. Informal. in poor physical condition.
10. troublesome or vicious; bad-tempered: a mean old horse.
11. Slang. skillful or impressive: He blows a mean trumpet.
http://dictionary.reference.com/browse/mean

contemptible may imply any quality provoking scorn or a low standing in any scale of values <a contemptible liar>.
despicable may imply utter worthlessness and usually suggests arousing an attitude of moral indignation <a despicable crime>
http://www.merriam-webster.com/dictionary/contemptible

because they felt that they were not chosen because they were unworthy in comparison