I'd say you can do exactly the same, it just has to be written out. So it won't be as compact as a matrix.
Go to Design - Rules (D, R), Electrical, Clearance, and add rules for pairs of classes. In this case, you'll have "where the first object is" one net class (the row in the matrix), and second from the intersecting matrix column. You can save some rules by using just one query against "all".
You can also add exceptions, like, IsPad finds all pads, and they can be assigned a lower clearance, which is sometimes necessary to get common footprints to behave (like the close spacing on a TO-220 -- you might have to route out slots between pads to meet UL, but Altium won't know about that gap as far as clearance).
Specify nets on the schematic using Net Class directives. (If these are ugly or obtrusive on the circuit, you can always encircle a pile of Net Labels with a blanket directive. Assuming you're naming the nets, which I would recommend.)
Tim