Shifter cable running beneath the bottom bracket without a sheath
Ghost shifting is generally caused by the frame flexing, not by friction in the cables.
Other causes can be a poorly fitting or too short cable housing. Something is causing the length of the cable between the stops to change. 

Cleaning the cable run and using a teflon coated shift cable won't hurt and might alleviate the problem if it's a combo of bottom bracket flex and sticky guide. When this
is the cause the problem tends to be very intermittent and only occurs when standing
on the pedals to climb. However, as Daniel R Hicks suggests, check the frame carefully for cracks. An aluminum alloy frame of that age that has seen a lot of miles is at the end of it's usable life. 

If you can't find any cracks, examine the cable housing runs carefully. The cable housing ends should not move at all in the stops when shifting or turning the handlebars. Check the derailleur hanger to make sure it's not loose. 

The part you are looking at is called a Bottom Bracket Cable Guide, but your's looks
just fine. They rarely wear out, shift cables aren't under much tension, so a plastic slider is plenty slippery enough. On an old enough bike, they are made of metal.