= Solution
Assume only <Standard Model> decay channels, negligible final-state <masses>, three <lepton> families, three <quark> <Color charge>[colours] and a <Unitary operator>[unitary] <CKM matrix>. The <Top quark>[top-quark] channels are kinematically closed. Summing the allowed <quark> channels gives $3\sum_{i=u,c}\sum_{j=d,s,b}|V_{ij}|^2\simeq6$ times one leptonic <decay width>[width], while the <leptons> contribute three. Neglecting <QCD> and <Electroweak interaction>[electroweak] <radiative corrections>,
$$
\Gamma_W\simeq9\Gamma_\ell=\frac{9g^2m_W}{48\pi}.
$$
The source's rounded CKM entries give almost the same factor; their tiny nonunitarity is not physically significant. Consequently
$$
\boxed{g^2=\frac{48\pi\Gamma_W}{9m_W}=0.4356\pm0.0083,\qquad g=0.6600\pm0.0063.}
$$
The propagated <Measurement uncertainty>[uncertainty] uses $\delta g/g=\tfrac12\delta\Gamma_W/\Gamma_W$, taking $m_W$ as fixed. It is the measurement <Measurement uncertainty>[uncertainty] within the stated tree-level approximation; omitted <radiative corrections> are an additional modelling limitation. In particular <QCD> increases the hadronic <decay width>[width] and lowers the inferred <Gauge coupling>[coupling] when included.
The printed electromagnetic comparison $4\pi/137$ is $e^2$, not the <probability amplitude> <Gauge coupling>[coupling] $e$. Compare like quantities:
$$
\boxed{\frac{g^2}{e^2}\simeq4.75,\qquad e=\sqrt{4\pi/137}\simeq0.303,\qquad g/e\simeq2.18.}
$$
Equivalently $\alpha_W=g^2/(4\pi)\simeq0.0347$ exceeds $\alpha_{\mathrm{EM}}\simeq1/137$. The <weak interaction> is weak at low <energy> primarily because of the massive <propagator>, rather than an exceptionally small fundamental <Gauge coupling>[coupling].
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