Is XPS already an old method? not a lot of new research is produced recently about it. Besides, you can carry out the same analysis by several cheaper methods. Do you think the chemical analysis by XPS is already over now, or XPS is getting not very important any longer?
That sort of depends on what you mean by XPS, what you mean by "old" and what you mean by "method". It can very well be the case that some parts of chemistry and solid-state physics have moved to other methods of analysis, so XPS does not get used as a tool all that often. Similarly, much of the core of XPS is established science, so there's not that much work on the essentials nowadays.
If you want to draw your conclusions straight from that, then sure, XPS is old hat.
However, there's a ton of very modern work on methods that consist of shining x-rays at a sample and measuring the energy of the photoelectron: the nearest to my field is attosecond transient absorption spectroscopy, but there's a huge body of FEL-based work, too. Is this XPS? Is it not? Who cares? Semantics is not science.
As to whether chemical analysis by means of XPS has dropped out of favour with chemists, you'd have to ask one of them.