I have a worksheet with the following contents in A1:G1
7 8 4 2 9 11 10
Formula
=SUMPRODUCT(MIN($B1:$G1-$A1)) (1)
As per my comment, to get the smallest difference between A1 and B1:G1 without using an "array entered" formula you can use INDEX to do what you were trying to do with SUMPRODUCT, i.e.
INDEX
SUMPRODUCT
=MIN(INDEX(ABS($B1:$G1-$A1),0))