And there are benefits for the slave in the Empire, e.g. the chance for rehabilitation into Amarr society as a citizen or the introduction into it as such.
I see slavery as merely a certain set of cultural norms regulating a particular form of dependent relationship between people.
There are many relationships in society where the balance of power between the partners in the relationship is unequal and not freely chosen. Marital relationship, parent-child relationships, warden-prisoner relationships, officer-grunt relationships, etc. etc.
In an age where getting pregnant was not really a choice, protecting women from getting pregnant without a 'partner' that was expected to help her give birth and raise children was very benificial. Even if it came at the cost of getting raped at times (within the marriage).
Having someone that inflicted damage on society removed from it temporarily and having others husband them (imprisonement) can be very benificial to society as a whole (if perhaps not to the prisoner).
And few question the benefit of the unequal and dependent relationship between children and those that raise them.
There is a law here which obligated everyone until the age of 16 to have full-time schooling. I can tell you that most children of 12-16 in modern western society would rather not have that (near daily) obligation visited upon them. However, its likely they will benefit from it. So can slave benefit from education given to them.
Is slavery an optimal means of providing benefits to such people? I don't think so. But that wasn't the question....
In this arena, the question becomes: what justifies the determination of one party being deemed "dependent."
Just to address your examples,
Marriage: If the arrangement is not freely chosen, then in this case I do see it as another form of slavery or subjugation. Usually this is seen in societies where one of the two sexes is seen as inferior with all manner of condescending rationalizations offered. While there is high correlation between this paradigm and other abuses, the tipping point for me starts at the basic act of whether both partners entered willingly or if one (or both) were refused free association.
Parent-child: Children are in many ways incapable of fully functioning and sustaining themselves without assistance. Different cultures have different views on when this changes (and different expectations on how to prepare them for this). Infants and toddlers are dependent for basic sustenance and physical well-being, children for safety and security, adolescents enter a period of turbulence in emotional growth and judgment. I think the most deviation occurs in the last period, some preferring to retain "control" through young adulthood, others preferring to let them loose at that point and rely on a more distant "guidance" from there. The legal requirement for schooling is based on the idea that a) society as a whole benefits from educated people and b) without education in a society where it is prevalent, a person may be far less capable of meeting their basic needs (can't get a job that provides the minimal necessities of sustaining life). Obviously, there's a lot of variables that can differ here.
Warden-prisoner: Assuming the prisoner was fully aware of the laws in effect, they freely chose to enter into this relationship by breaking them. Again, room for debate arises out of whether the laws themselves were aligned towards common societal interests or designed to extract conformity for the benefit of a few (imprisonment for voicing a dissenting opinion, political prisoners, etc). This could also be the result of being captured in an armed conflict, which I'll expand upon below.
Officer-grunt: Again, a relationship that may or may not be the result of a voluntary agreement. In an all-volunteer military, you chose to enter into this relationship from the very beginning. Also, depending on the military in question, there may be many benefits you enjoy as a result of this association. In the U.S. you can receive assistance in pursuing higher education, an honorable discharge looks great on a job application, you have the camaraderie and respect of fellow service members and access to social services available exclusively to veterans. On the other end of the spectrum would be a draft or impressment-based military that offers nothing in return. Which would basically be a form of slavery in which you were expected to place yourself at great personal risk without any reciprocal benefit or compensation. There's probably some grey areas in there where some threatening external force that would be detrimental to society exists and able members of the community are required to submit to service (WW2, for example). While it could be argued that free association was removed, at least in this case some benefit exists for those who are required to participate (assuming the threat was real and not manufactured or over-stated). Also in this specific example, while retroactively put into place, many additional benefits were given to those who served in the conflict and was partly responsible for a further increase in overall societal well-being (benefits given to veterans and their families helped build the middle class in America).
So there seems to be some overall guidelines here:
1) Is the relationship a result of free-association or not
2) Do all parties to the relationship receive benefits at least partially consistent with their relative efforts
3) What dependencies exist that justify one party existing in a lesser role
If one party has no say in their status, can't be shown to have any real dependency in the absence of coercive force or societal whim and remains limited in their share of communal wealth while doing the bulk of the actual value-increasing work required to sustain that wealth...
I'd call that slavery based on definable, measurable terms.