I think the closest thing to the Sprague-Grundy theorem in the partizan normal-play case is the corollary of Theorem 69 in *On Numbers and Games*. Every short game* has a unique canonical/normal form where all "dominated options" are deleted and all "reversible options" have been replaced and all options are written in their canonical forms. For the games which happen to be impartial, their canonical forms are the standard forms for Nim heaps: $\left\{\left\{|\right\}|\left\{|\right\}\right\}$ for the Nim heap of size 1 (often denoted $*$), etc.

If you don't have ONAG at hand, you can read about dominated and reversible options in *An Introduction to Conway's Games and Numbers*. Their theorem 2.25 is essentially Theorem 69 from ONAG, but has a subtle error: it claims that there is a *unique* example in each equivalence class with no dominated or reversible options (as opposed to a good unique canonical choice).

Here is a counter-example: $\left\{ \left\{|\right\} | \right\}$ is $\left\{0|\right\}=1$ and has no dominated or reversible options. But $\left\{ \left\{*|*\right\} | \right\}=\left\{ \left\{\left\{\left\{|\right\}|\left\{|\right\}\right\}|\left\{\left\{|\right\}|\left\{|\right\}\right\}\right\} | \right\}$ is equivalent to $\left\{0|\right\}=1$, and it *also* has no dominated/reversible options.

*A game is short if it has only finitely many positions. The Sprague-Grundy theorem usually applies to the short impartial games, stating that they're each equivalent to a single finite Nim heap.