How should I respond to a reviewer comment that I didn't make changes when I did? I received an email from the editor, including a quote from the reviewer saying "I regret to inform you that the authors failed to address the points I raised in my previous review of this manuscript, in this case, any further comments on this manuscript is pointless."

I sent them an email to ask about the point that we failed to address because I made the changes in the manuscript that the reviewer ask for it. The reviewer said that the authors failed to update the reference list. I add 3 more references to support the old one because he said in his review paper that if the authors don't want to omit old references at least can use them together with more recent ones.

This is the reviewer's comments on my original manuscript: 


  The references list needs to be updated. There are old references (1980s – 1990s) that can be replaced with more recent ones. Please see below a number of suggested recent papers that can replace old references. If the authors are not willing to omit old references at least can use them together with more recent ones.


And this is his comment after I updated my manuscript:


  Unfortunately, the authors failed to update the reference list, and failed to respond to these comments. There are no changes on the manuscript. Authors should address any comments given by reviewers, in a point-to-point response; even if they do not want to consider the comments or suggestions from reviewers they must address their reasons for not considering these comments and suggestions. Given that there are no changes on the manuscript, and there is no point-to-point response from the authors, this review is pointless. Thank you for given me the opportunity to review this manuscript, I leave the final decision to you, since there is no response from the authors.


Please advise me if there is anything that I should be doing? The other reviewer recommended that my manuscript be accepted "as is."
Treat it as a mistake.  

It sounds like the reviewer may be looking at the old version of the manuscript, either due to their own mistake or someone else's.  Alternatively, the reviewer might not have noticed the changes (which sound somewhat minor).

You should assume the reviewer is simply mistaken and respond with that in mind.  Something like:


  Sorry, there seems to be a misunderstanding.  I did indeed update the paper with changes in response to the reviewer's request...


Did you also include a point-by-point response to the reviewer?

From the situation you describe, it sounds like you may not have.  Even if you agree and make the changes, you should still say so, and state what you have done.  For example:


  The references list needs to be updated. There are old references
  (1980s – 1990s) that can be replaced with more recent ones. Please see
  below a number of suggested recent papers that can replace old
  references. If the authors are not willing to omit old references at
  least can use them together with more recent ones.
  
  We have added several more recent references.  Thanks for the suggested papers.


This should remove the possibility of such a misunderstanding occurring.  

If you did not do so initially, include it now when you respond to the reviewer's objection (and I would apologize for not making the changes clear in the first place).