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I am currently reviewing a paper, which has this statement in the acknowledgements:

The United States Government retains and the publisher, by accepting
the article for publication, acknowledges that the United States
Government retains a non-exclusive, paid-up, irrevocable, world-wide
license to publish or reproduce the published form of this manuscript,
or allow other to do so, for United States Government purposes.
Source

As a reviewer, I could simply ignore it. However, it seems rather weird to me, since usually after acceptance you have to sign a form which deals with exactly this kind of right transfer / copyright etc. The editors and referees do not have any legal power over this anyway.

Does my role as a reviewer also include to mention this to the editor who should forward it to the publisher, or should I simply ignore it, on the risk that this statement potentially collides with the journal policies?

The article (i.e. its contents and references) are within your remit as a reviewer.

Checking copyright details and investigating any the legal ramifications will not be relevant to the review you should be doing.

You can mention it to the editor in your report, but you do not need to. Your job is to evaluate the correctness and other merits of the manuscript's contents, not to deal with issues such as copyrights. Those are the job of the editorial staff. Moreover, the editors and publisher are probably experienced in dealing with the copyright requirements of government employees and should know to be on the lookout for situations like this.

If you want to mention it, I would suggest saying something like:

I noticed an statement about copyright in the acknowledgements, something that I had never seen before. I just wanted to bring this to your attention so it does not get missed.

I think it is pretty unlikely that the editor isn't already aware of this, but, yes, you should mention it somewhere in your report to the editor. It amounts to a restriction on what the publisher can claim as "reserved rights".

It says, in effect, that if the publisher, accepts this article (and obtains its copyright) the publisher must thereby grant the U.S. Government a license of a certain sort. This means a conditional transfer of copyright.

My guess is that this is fairly standard for work produced by the government and in some cases, work produced by others on government grants. The government doesn't want to create a work and then have to pay to use it internally (i.e. for U.S. Government purposes).

It is your prerogative what to do about this, but it is not your legal duty to review the copyright procedure. It is a publisher's legal duty.

What you mention about standard procedure about copyright transfer agreements or licenses is not obvious, given that it's dependent on the publisher's procedure what this entails. Open access publishers, for example, do not require any transfer or exclusive license. Most publishers share their procedures online, but most do not check this (nor is comprehension of these agreements obvious, see also this study)

U.S. federal works are not copyrightable under 17 U.S.C. § 105, so it makes perfect sense the authors state this if they are federal employees. Previously, works by federal employees (for example Barack Obama in Science) have had their copyright claimed by publishers upon publication, which is against this law.