Why is it only one of four batteries (Li Ion) is drained?
at least when I use Li-Ion, non-rechargeables


Do you mean when using when using conventional alkaline batteries?  Li-ion cells have a terminal voltage ranging from 3.2 to 3.7V, depending in the specific chemistry, and I'd be really surprised if you had a programmable remote from 1999 that uses Li-ion cells.

There are one or more things at play here--

1)  In a series string of cells, there will nearly always be one cell that is depleted first.  The usable capacity of each cell varies a bit due to manufacturing tolerances and a number of other factors, so there is always going to be one of the four that has the lowest inherent capacity and is the first to run out.

2)  Some devices require multiple voltages internally, and rather than adding the cost of a converter, they simply tap the cells at a convenient point.  For example, imagine a device that needs 1.5V and 6.0V.  All four cells are drained in series for the 6V load, and one of the cells is drained an additional amount to supply the 1.5V load, sharing a common ground potential.  For a programmable remote, this may be the case if the remote uses 1.5V to retain its memory or show status on an LCD, while using 6V for its transmit functionality.  If the cell that dies first is always installed in the same position in your battery tray, I'd say that this is a likely scenario.