I've skimmed the report you linked to, and I really don't see the contradiction. E.g. look at the quote below, taken from several on inequality:
"The second WBG goal of boosting shared
prosperity is new and opportune. It shifts the focus in
evaluating economic development from average income
growth to income growth of the bottom 40 percent. Indicators
proxying the socioeconomic status of the bottom
40 percent of the population, have shown little improvement,
even though the growth of incomes of the bottom
40 percent of the population has not been slower than
that of the general population in many countries. This
growing inequality in basic living standards is worrisome".
I don't see anything that contradicts the Oxfam report, while there are some comments that seem broadly in line with it. Overall, the broad thrust of both seem in roughly the same direction, although they do take different views.
Again the inequalities in income shrinking progressively shown in the interactive presentation is between countries. It looks at incomes below 100k USD, which is not particularly relevant to a debate on the top global 1%.
I'm sure there's a debate to be had on how much inequality restricts growth. Perhaps it's not correct when Oxfam says that reducing inequality could improve the overall size of the pie. But I see little in your links to contradict that at first glance. Maybe you could point out more specific grounds for your views?