While CERN's Large Hadron Collider (LHC) is primarily a high-energy proton or heavy ion collider, it can also be used as a high-energy photon collider. This is possible because the highly boosted electromagnetic fields surrounding the circulating ions behaves like a flux of photons. A search for the process $\gamma\gamma\rightarrow W^{+}W^{-}$ was conducted in the 139 fb$^{-1}$ of proton-proton collision data collected in LHC Run 2 between 2015 and 2018. Events were tagged using the $e^{\pm}\nu\mu^{\mp}\nu$ decay channel of the $W^{+}W^{-}$ system, where the event was determined to be photon-induced due to a lack of charged hadronic activity near the leptons. The process was observed with a significance of 8.4$\sigma$, with a measured fiducial cross section of $3.13 \pm 0.31~(\mathrm{stat.}) \pm 0.28~(\mathrm{syst.})~\mathrm{fb}$. This fiducial cross-section agrees with Standard Model expectations. A strategy to improve the \yyWW~measurement with the use of a novel low-\pt~tracking algorithm in ATLAS is also presented. The use of low-\pt~tracks improves the rejection of QCD-induced backgrounds to \yyWW, leading to an expected increase in statistical significance of 3--4$\sigma$.