If I have understood your requirement correctly the following would return a numerical value from Column3:
= MINIFS( Table1[Column3], Table1[Column1], Criterion1, Table1[Column2], Criterion2 )
Out of curiosity, why do you specify a non-CSE formula?
It is possible to get the benefit of an array formula without having to control the simultaneous movement of 3 digits if you use named formulas. By using Name Manager to define the formula 'matchingRow' to refer to
= MATCH( 1, (Table1[Column1]=Criterion1)*(Table1[Column2]=Criterion2), 0 )
one obtains a non-CSE formula
= INDEX( Table1[Column3], matchingRow )
which will return text or numbers from Column3.