Sulfinate R/S configuration
According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), the trigonal pyramidal centre of the sulfinate group is converted to a tetrahedral centre using a phantom atom of low priority.

P-93.3.3.2 Trigonal pyramid
The configuration of molecules containing a trigonal pyramidal center (TPY-3) is described in a similar way to that of tetrahedral centers (T-4) described above in P-92 (see IR-9.3.4.3, ref. 12). The tetrahedral configuration is achieved by adding a phantom atom (0) to the central atom perpendicular to the base of the pyramid. (…)
Traditionally, sulfoxides have been considered as a tetrahedral system composed of a central atom, ligands, and a lone pair of electrons (or phantom atom). No polyhedral symbol is used.

 

P-93.3.4.1 The chirality symbols ‘R/S’.
The stereodescriptors ‘R’ and ‘S’ (as defined in P-92.2) are used to indicate the absolute configuration of a trigonal pyramidal system discussed in P-93.3.3.2 (see Rule IR-9.3.4.3, ref. 12). A phantom atom of low priority, and not a pair of electrons, is used to create the tetrahedral configuration permitting the use of ‘R/S’ stereodescriptors in the manner described for tetrahedral stereogenic centers. As no locants are present, the name following the stereodescriptor is placed in parentheses, or bracket, according to the required nesting order.

The examples given for this rule in the Blue Book include ethyl (R)-(4-nitrobenzene-1-sulfinate), which confirms that this rule is applicable to the similar compound methyl (S)-methanesulfinate, which is given in the question.
Notably, an equivalent rule also exists in the current version of the current version of Nomenclature of Inorganic Chemistry – IUPAC Recommendations 2005 (Red Book).

IR-9.3.4.3 The R/S convention for trigonal pyramidal centres
Molecules containing a trigonal pyramidal centre (TPY-3) may exist as a pair of stereoisomers. The configuration of this centre can be described in a similar way to that of a tetrahedral centre. This is achieved through notional placement of a ‘phantom atom’ of low priority in the coordination site that would create a tetrahedral centre from a trigonal pyramidal centre. The centre can then be identified as R or S by the methods described above.
The use of some bonding theories leads to the placement of a lone pair on a trigonal pyramidal centre. If this is done, the absolute configuration of the centre is also described by the R/S convention, in this case by placing the ‘phantom atom’ in the site that is occupied by the lone pair. Examples of this practice may be found in the description of absolute configurations for sulfoxides in which the alkyl substituents are different.

After placement of the phantom atom, the R/S convention for tetrahedral centres can be used. Rules for the tetrahedral configuration of elements other than carbon are given in Section P-93.2 of the Blue Book. In particular, the rule for compounds containing sulfur refers to the rule for similar phosphorus compounds.

P-93.2.5 Sulfates, sulfonates, and related compounds
Sulfates, sulfonates, and related anions are treated in the same way as phosphate anions (see P-93.2.4). (…) Sulfoxides are discussed in P-93.3.3.2.

The corresponding rule for compounds containing phosphorus reads as follows.

P-93.2.4 Phosphates, phosphonates, and related compounds
The ‘$\ce{P=O}$’ bond, as conventionally written in phosphates, phosphonates, and related compounds, is considered as a single bond, as there are already four atoms or groups in the tetrahedral configuration. Similarly, the formal arrangement of charges is not considered when determining the configuration of a chiral molecule. As the stereodescriptors ‘R’ and ‘S’ describe the entire structure, either a salt or an ester, the full name is placed in parentheses to denote the global configuration.

Therefore, the analogous ‘$\ce{S=O}$’ bond in the sulfinate group is considered only as a single bond since the tetrahedral centre of the sulfinate group with an attached phantom atom already has four groups. (Note that this is a deviation from the usual Sequence Rules for the Cahn-Ingold-Prelog (CIP) System. Using the Sequence Rules, double bonds are normally split into two bonds with duplicate representations of the atoms at the other end of the double bond.)
Thus, for the compound given in the question, the $\ce{-O-CH3}$ group ranks higher than the $\ce{=O}$ group. This leads to the configuration S and the systematic name methyl (S)-methanesulfinate.