Normally a person is beset by many natural tendencies, or animalistic desires. A Jew is expected to channel and master these desires until he rules them, rather than the default in which they rule him. One trick we have in this near-insurmountable challenge is that we can convince ourselves that our needs are not our own, but are external to us, borrowed perhaps from someone else. Since the yetzer hara (evil urge) encourages us to be selfish and unconcerned with the needs of others, if we convince ourselves that our own needs are "borrowed" from others, then naturally we will disdain them.
This seems very weird and unnatural, not to mention ridiculous, to think of our needs as someone else's needs. But, there is a kernel of truth there, in that these desires for worldly pleasure don't actually originate with the person, but rather with his/her yetzer hara.
Once we have worked on ourselves and have begun to conquer this stage, the Noam Elimelech's advice really starts to pay off. Since our own needs are as devalued as the needs of others, the work to make the needs of others more important, if not as important as our own personal needs becomes a lot easier. Instead of fighting an uphill battle we've now leveled the playing field.
The question, to me, becomes why did the Noam Elimelech choose to bring out this teaching from passukim related to ma'aser and bikkurim. (both of which are offerings brought to HaShem from the blessings He has bestowed upon us.) Perhaps it is because when we recognize that everything we've received is from HaShem, and not ours to begin with, we can apply this lesson not only to the positive things we've recieved but also the negative ones, like the yetzer hara, for example. After all, everything is from HaShem.