Mind that you can use an expression as the replacement string in the substitute command (:s). When the replacement string starts with \= it is evaluated as an expression.
Here, one possible solution is
:let i=1 | g/^x'\d\+'/s//\=i/ | let i=i+1
It finds all occurrences (one per line) of the ^x'\d\+' pattern and replaces it with the value if i that is incremented each time the match is found. As has been noted in comments, the | is a part of the g replacing "code", as "| is used to execute more than one command at a time".
Another solution is using the line() command (taking into account that your file has a header top line, so you should actually subtract 1 from the value returned with line()):
%s/^x'\d\+'/\=line('.')-1/
The ^x'\d\+' regex matches
^ - start of a line
x' - x' string
\d\+ - 1+ digits
' - a ' char.
There are other interesting "increment number in regex" examples at the Using an expression in substitute command page:
- Number all the lines in a file (insert line number followed by a tab):
:%s/^/\=line('.')."\t"/
- Number a range of lines (from line 10 to line 20):
:10,20s/^/\=line('.')."\t"/
- Number a range of lines sequentially starting from 1:
:let counter=0|10,20g//let counter=counter+1|s/^/\=counter."\t"
- Number all the paragraphs in range starting from 1 (assuming the paragraphs are separated by one or more blank lines):
:let counter=0|1,20g/^$\n^\s*[^\s]/let counter=counter+1|+1s/^/\=counter."\t"
Note: The above command does not work for the first paragraph in the file if there is no blank line above it.