Yes, you can explicitly manage the stack. You still consume memory at the same rate, but now it is a heap-allocated stack that is programmatically controlled, instead of a stack-allocated stack that is automatically controlled.
The issue is either:
* whatever the parser is doing is already tail recursive, but not expressed in C in a way that doesn't consume stack. In this case it's trivial, but perhaps tedious, to convert it to a form that doesn't use unbounded resources.
* whatever the parser is doing uses the intermediate results of the recursion, and hence is not trivially tail recursive. In this case any reformulation of the algorithm using different language constructs will continue to use unbounded resources, just heap instead of stack.
It's not clear how the issue was fixed. The only description in the blog post is "It used the same mechanism of delayed interpretation" which suggests they didn't translate the existing algorithm to a different form, but changed the algorithm itself to a different algorithm. (It reads like they went from eager to lazy evaluation.)
Either way, it's not recursion itself that is the problem.