Looking at your board it appears that Slot#1 and Slot#2 (colored black?) should be used for the memory -- this ASUS board has 3 memory slots instead of the usual 4 and they are organized differently. Alternate is not right here.
A good article discussing Dual-Channel RAM,
Everything You Need to Know About Dual Channel
Dual channel is the ability that some memory controllers have to expand the width of their data busses from 64 to 128 bits. Considering that everything remains the same (clock speeds, for example), the memory maximum theoretical transfer rate is doubled by the use of this technique.
Memories based on DDR (Double Data Rate) technology such as DDR-SDRAM, DDR2-SDRAM and DDR3-SDRAM transfer two data per clock cycle. Because of that they achieve double the transfer rate compared to traditional memories (such as the original SDRAM) running at the same clock rate.
For dual-channel technology to work you need to have an even number of memory modules on your system (assuming that your AMD CPU or Intel chipset support this technology, of course). If you install just one module this technique won’t work because memory will still be accessed 64 bits per cycle. In other words, dual channel works by accessing two memory modules in parallel, i.e. at the same time.
Because the two modules are accessed at the same time, they must be identical (same capacity, same timings and same clock rate).
Finally, this is described with more words in the article,
If you have a motherboard with 4 slots, and you own two similar memory sticks compatible with your board, it is critical to place them on the correct two slots (usually alternate slots). The board is wired to use them in dual-channel mode correctly on these placements. Suitable slot pairs are usually colored the same to remind you about this.
So, YES, you should care. You have the right memory (DDR two matched units) and you are running single more just because of incorrect memory placement.