This is the Lump of Labor Fallacy. There is not a fixed number of jobs in the economy, and eliminating a particular job does not mean "one less job".
I think you mean that it doesn't necessarily mean one less job. There is a possibility it means that. For example, the business could pocket the extra profit and hoard it rather than reinvest.
Either way, someone will have more money in their pocket, and will spend that money on other goods, services or investments, generating jobs elsewhere in the economy.
As stated above: there is no requirement that the money saved gets spent anywhere. The business could pocket the profit and do nothing with it.
This is actually a growing concern of late, as we have seen a number of top businesses start to hoard cash - the best example of which would be Apple, which is sitting on over $200 Billion.
Dead end make-work jobs are not "good for the economy", and the point of work is to create goods and services, not to "keep people busy".
It's certainly the ideal that everyone works to create more wealth overall. We can hope that automation starts to open up new markets like technological advances of the past did, but we should prepare for the possibility that it won't.
If the worst happens, and we end up with a growing group of poor, hungry individuals, then make work projects could be better than inviting future civil unrest. That's somewhat of a moot point, though, as there is plenty of neglected infrastructure that we as a country could start training and paying people to repair.