I suppose this depends on how narrow the tasks/skills in question are, as there are various ways to measure general intelligence.

For example, there was a study indicating that playing Starcraft improved multi-tasking ability:

> Using a meta-analytic Bayes factor approach, we found that the gaming condition that emphasized maintenance and rapid switching between multiple information and action sources led to a large increase in cognitive flexibility as measured by a wide array of non-video gaming tasks.

I suppose here the rub would be, exactly how specific or different from the video game were these "non-video gaming tasks"? If they're broad enough that we consider them reasonable measurements of overall multi-tasking ability, then yes, playing Starcraft maybe made you smarter in one particular dimension. If they're all very similar to the game itself, and broader measurements found no change, then no.

> To determine changes in cognitive flexibility that occurred as a result of video gaming, participants completed a battery of psychological tasks at pre-test and post-test (at 40 hours of gaming). The battery included measures that address cognitive flexibility as well as measures of unrelated constructs. Measures of flexibility included the Attention Network Test (ANT) [28], Stroop task [29], task switching [30], a novel multi-location memory task, and test of Operating Span (Ospan; distinct from simple counting memory span) [31], [32]. These are classic measures of cognitive flexibility in that they require the switching or coordination of cognitive processes in order to successfully navigate the task at hand. For example, the task switching paradigm involves switching between two different stimulus identification tasks. All the measures in the cognitive flexibility task group assess the ability to coordinate attentional processes between two or more concurrent or alternating operations. Measures of predicted unrelated constructs included the balloon analogue risk task (BART) [33], visual search task [14], information filtering task [34], and WAIS-IV digit span memory task [35], [36]. These tasks were chosen to help delineate the specific hypothesis that RTS training would lead specifically to cognitive flexibility enhancements given that RTS game play stresses fast-paced switching and coordination of decisional processing. The visual search task and the information filtering task were chosen due to their use in previous action video game research [12], in order to differentiate RTS training from action video game training. BART and the digit span memory task were chosen due to further delineate cognitive flexibility from the broad domains of risk sensitivity and general memory. Participant groups were equated on the Multimedia Multitasking Index (MMI), a measure of the amount of time an individual spends simultaneously engaged in more than one form of media [37]. Consistent with best scientific practices and openness, the task grouping and analysis strategy were determined and publically disclosed [38] prior to data collection.

Gonna be honest here, that all sounds rather impressive to me but I have no idea what those tests actually entail.

https://journals.plos.org/plosone/article?id=10.1371/journal...