I'll try to keep this simple for you:
When they are comparing paleoclimate to today, we don't use 'year-by-year' resolutions, we use decadal resolutions which iron out the wrinkles.
YOUR paper was from ~2006; I believe they used 'reference data' for current temperatures up to the mid/late 1990s.
MY link is from ~2014, so they have another decade OR MORE of data for comparing temperatures to the 2000 year dataset. (NOTE that 'reference' papers like the one you linked are NOT original research, they are SUMMARIES of OLDER papers)
Look at this graph and see what global temperatures have done in that past 10+ years (using decadal smoothing):
So, 10-15 years ago (circa: the origin of the data referenced in your 2006 paper) the average temperature MAY HAVE OVERLAPPED the error bars from the prior peaks in the 2000 year record; TODAY those temperatures are EXCEEDING the error bars, as we are AT LEAST 0.2°C WARMER:
Now, we CAN see the difference.
Again, this is why we look at the more RECENT data and rely less on OLDER comparisons which are based on OUTDATED datasets.