r caret predict returns fewer output than input

I downloaded your data and found what explains the discrepancy.

If you simply remove the missing values from your dataset, the length of the outputs match:

testRpart <- predict(fitRpart, newdata = na.omit(dtest))

Note nrow(na.omit(dtest)) is 1103, and length(testRpart) is 1103. So you need a strategy to address missing values. See ?predict.rpart and the options for the na.action parameter to choose what you want.