Given a journal policy that authors must share original data, am I free to use this data without granting original authors authorship?

I'm not a fan of "mandatory authorship" on published information: I feel that once something is published, one should collect one's rewards by means of citation rather than by strong-arming people into giving you an authorship. Mandatory authorship on already-published data feels to me too much like a form of salami-slicing on a dataset.

That said, the journal's policy does not appear to say anything at all regarding authorship. Therefore, the default position would seem to be that the authors must share the data with you (as mandated by the journal), but are also free to require authorship as "payment" for sharing.

The journal, however, may feel that this goes against the spirit of their data sharing agreement, and if so, then you may be able to obtain the data without being coerced into authorship. I would thus recommend, like @BrianBorchers notes in the comment, that you write to the chief editor(s) and ask for a ruling.

Your argument here strikes me as incredibly flimsy. As you point out, the data is in fact available, just with the restriction that it cannot be used in further papers without offering coauthorship, and that restriction in no way contradicts the journal's stated policies.

It's not clear whether it violates the intent of the policies. One argument that it doesn't is that the journal specifically says this data must be available "in a form which allows for verification and replication of the results in the paper", which is different from allowing use in other work. Furthermore, the policy says "reasonable request", which suggests that some requests could be considered unreasonable. It's not 100% clear what the policy's authors had in mind (presumably requests for materials could more easily be considered unreasonable), but they certainly didn't say "everyone is entitled to the data and can do whatever they want with it, no questions asked".

So it seems to me that the written policy offers no support for your position.

I do not think it's fruitful to ask the journal editors for permission. Even if they declare that these restrictions are not what they had in mind, they have no authority to impose this interpretation retroactively.

If you try to use the data without offering coauthorship, there's a real risk that the data generators could file a misconduct complaint against you with your university, a relevant professional society, or the journal you end up publishing in. If I had to adjudicate such a complaint, I expect I would decide in their favor.

This is not to say that they are behaving reasonably, and I agree that jakebeal that this is a questionable practice. However, you haven't found a loophole that justifies ignoring their request.