The evidence is fairly weak.
But granting that the Chinese of that period did in fact do this, it was no more significant than the Viking or Irish Monks who also sailed to North America early:
IOW, not very important.
It was Columbus who led the way for significant change.
According to the book itself, the Chinese effort was suppressed by the Chinese Imperial Govt., and all or nearly all records destroyed.
The Chinese colonies, if there were in fact any, were assimilated into the local populations and left no meaningful independent record.
Ed