EDIT: Emil points out serious issues in the notion of unambiguity I give below, to the point that it's clear this notion isn't appropriate. (OP, I think you should un-select this answer and select Emil's answer.)
Only a partial answer: I'm no expert in this area, but it seems that the definition of ambiguity can be extended in a natural way to arbitrary context-sensitive grammars.
Note: I believe - although correct me if I'm wrong - that the thesis the OP refers to is that of Saichaitanya Jampana (https://shareok.org/bitstream/handle/11244/8173/Jampana_okstate_0664M_1373.pdf?sequence=1); and the specific part referenced is page 17.
Quick overview of the basics: A general formal grammar is a tuple $(N, \Sigma, P, S)$ with $N$ and $\Sigma$ disjoint finite sets (nonterminal and terminal symbols respectively), $P$ a finite set of production rules (i.e., expressions of the form "$p\rightarrow q$" with $p\in (\Sigma\cup N)^*N(\Sigma\cup N)^*$ and $q\in (\Sigma\cup N)^*$), and $S\in N$ a fixed symbol; the language $L(G)$ attached to a grammar $G$ is the set of strings in $(\Sigma\cup N)^*$ which can be derived from $S$ using finitely many applications of rules in $P$. Iff $p$ appears as the left hand of some rule in $P$, say $p$ is convertible. Now, a context-free grammar is just a grammar satisfying a special condition: that whenever $"p\rightarrow q$"$\in P$, we have that $p$ is a single symbol from $N$.
The wikipedia page - and most references I could find - on ambiguity then defines ambiguity only for context-free grammars: a context-free grammar $G$ is unambiguous if every $p\in L(G)$ has a unique leftmost derivation (that is, a sequence of applications of rules in $P$ to the starting symbol $S$, concluding with $p$, such that at each stage the leftmost nonterminal symbol is converted). Since in arbitrary formal grammars, derivation rules need not be applied to only individual nonterminal symbols, this definition doesn't carry over meaningfully.
However, it seems that it can be easily generalized: for an arbitrary formal language $L(G)$ and $p\in L(G)$, a leftmost derivation of $p$ in $G$ is a derivation of $p$ in which at each stage, a rule from $P$ is applied to the leftmost convertible substring. So, e.g., if (with $x, y, z, w\in N$) $P$ contains the rules $xy\rightarrow yz, z\rightarrow wy, yw\rightarrow x, wy\rightarrow z$, then $$xy\mapsto yz\mapsto ywy\mapsto yz$$ is not a leftmost derivation of $yz$, since the leftmost convertible substring of the penultimate string is $yw$, not $wy$.
Note that this notion of ambiguity extends that for context-free grammars, since the convertible strings in a context-free grammar are all individual nonterminal symbols.
Finally, note that this notion of ambiguity (just like the standard one) applies to grammars, not languages. For a language $L$, the relevant notion is "inherent ambiguity": $L$ is inherently ambiguous (within a certain context of languages, e.g. context-sensitive) if it is not generated by any non-ambiguous grammar (again within that context).
Of coure, I'm not sure this is the actual definition, but I strongly suspect this is what S. Jampana means. Regardless, the notion of inherent ambiguity explained above is that used by Jampana: see page 17.
And, of course, I don't have off the top of my head a proof of why the languages he mentions are in fact inherently ambiguous, so this isn't a complete answer, even if I do have the right notion of ambiguity.