The definition that you have provided seems to be an unnecessarily broad definition. In that sense, it seems that even your own disapproval of Libertarianism is itself a religion. It seems from a quick search that most definitions include further restraints, often including some strongly held belief in something super natural, which Libertarinism does not have.
Also, you seem to be conflating Libertariansim with free market Capitalism. While this may be an outcome of Libertarian political ideology, it is not the cornerstone of it. The Libertarian ideology doesn't necessarily aim for people to have improved lives, but is a stance on what the government itself has or should have a right or responsibility to do. This may in turn be believed because of an appeal to a some more core belief system which may or may not appeal to the supernatural, etc.
Since you mostly reference free market Capitalism, consider that it is not some mystical thing or some blind emotional appeal. It is a prescription for a healthier economic system from the reference of Austrian Economics. That system invented the theory of marginality and solidified value theory in a concrete and predictable way. In that understanding of economics, value is related to the utility of a good or service (as opposed to the amount of labor used to obtain it or some historical value, and so forth), and so the only way to accurately or practical way to calculate it is to remove artificial constraints on the market. Thus, if you want to most accurately spread resources based upon utility, you should remove government constraint.
Free market Capitalism does not suggest that it will change what people value, and it doesn't directly attempt to claim that it will make lives better. It doesn't claim that it will solve all of our problems, and there is no appeal to magic or other unseen forces. It is simply one suggested policy about how to best address the problem of scarcity based upon a still popular economic model. So, I would say that it not only is not a religion based upon most sufficiently narrow definitions of religion, but it seems to also not be so based upon what seems to be your intuitive understanding of religion.