Yes - at least one (inch) link. See the Campagnolo diagram I shared earlier/upthread.
Your 53-39 and 13-26 set up is within the spec for this RD (I think 26t max).
But just shortening the chain may not sort your actual issue which is how high the guide pulley wheel is running.
I don't run Campagnolo but I have a spare part groupset (9sp and post 2001 like yours, bought in case my daughter's bike needed spare items (2014)) but irritatingly can't find the box to check its RD physically).
Searching offers this clue as to what might be an improvement:
"The pulley cage will need to be removed and then the pivot bolt that holds the inner plate to the derailleur will need to be removed. The spring inside (M) will have to be installed correctly and then the inner cage rotated to the proper position."
View attachment 730222
Obviously there is 'take it apart and can't get it back together again' risk.
Campagnolo recommends using a short cage derailleur with a maximum cassette cog size of 26 teeth even though it will [in practice] shift to a 29 tooth cog. 9 and 10 speed rear derailleurs use the same three cage lengths; 55, 72.5 and 89 mm (pulley wheels c-c) with a . chain wrap value of 27, 36 and 39.
For a 39/53 and a 13/26 combo you need a minimum CW of 27.