I don't really have an opinion on whether or not this is the main or even a reason for the evolution of senescence and death, but it is certainly not nonsense.
Death can indeed be good for a species. Diversity is always good and the death of the elders allows phenotypes that have been selected for more recently to take hold in the gene pool. If the young need to compete with the old, this will make it harder for them to grow and reproduce. In situations with a limited food supply, having to support old individuals who can no longer forage/hunt for themselves will be a strain on the species/society/pod or whatever it is we are looking at.
Therefore, genotypes that encourage the death of elders who are past the age of reproduction could be selected for. This does not contravene the selfish gene hypothesis at all, these individuals have already reproduced, the selfish gene no longer 'cares' about them. The main idea of the selfish gene hypothesis is that the genes themselves 'want' to be passed on, not that the genes 'want' to save themselves. Once their host has reproduced, they loose interest so to speak.
The selfish gene theory is just a conceptual tool, it should not be taken literally. It does not suggest that genes are actually selfish or in charge of their own evolution in any way. It is just a useful approach to take when studying evolution and was instrumental in our understanding that the gene (the nucleotide actually) and not the individual is the smallest unit of selection.
Anyway, in the strictest sense, the statement in your question is absolutely compatible with the selfish gene hypothesis. If you can no longer pass your genes along, you are useless and just a drain on the species, why should you keep living?