If you're interested in how the models behave over a specific part of the historic record, that mismatch can be a problem, but there are several approaches to dealing with it. You can, for example, subtract out the influence of things like volcanoes and ocean circulation to see what the climate is doing without them. Or, rather than letting your model generate its own ENSO, you can force it to replay historic events in order to see what those do to the temperatures.
The new paper adds an additional approach to handling the problem: simply run a bunch of models and pick those that, by accident, accurately reproduced the ocean's chaotic behavior. The authors started with the CMIP5 collection of climate models and selected the 18 models that include an ocean simulation that's sophisticated enough to provide data on the state of ENSO and other ocean behavior. They started these 18 models in 1880 and used historical forcings (solar activity, greenhouse gas concentrations, etc.) up until 2005, then switched to a standard emission scenario until stopping the models in 2012.
If you look at the four models that were the worst at reproducing ENSO behavior, then you'd think climate modelers were incompetent, as these models all showed rapid warming from 1990 onward. But, if you picked the four that had the best match to real-world ENSO data, then you see exactly what reality produced: a relatively slow rate of warming starting at about the beginning of the century.
The match isn't perfect, as the models leave out other forcings, like volcanoes, and they don't get all the details of the ENSO exactly right. But it's certainly another piece of evidence that ENSO activity has been critical for the recent behavior of our climate system.
Ars talked to climate scientists Gavin Schmidt and Michael Mann, who both emphasized that the new paper is in keeping with a variety of other studies that have come out in the recent past, with Mann saying, "This looks like a thoughtful and careful analysis that adds further weight to other recent studies (including our own recent GRL Frontier article) confirming that the temperature trends of the past decade do not, as some have claimed, contradict model-predicted global warming. The so-called 'speed bump' in global warming is consistent with the expected random fluctuations associated with natural, internal climate variability."