Edit: I decided to add a foreword since I don't think my answer was clear with my intent. I dont think OP's answer is as cut and dry as 'such and such manga was the first isekai with video game skills' I think it's more of a gradient over time. We have 'stuck in a video game', 'in a video game world' and then 'in a fantasy world with video game elements. Where the start of the final one is, is hard to say. My answer isn't that Sword Art Online is the first isekai with video game elements, rather that the start of this trend occurred after SAO came out. It was the catalyst.
Original Post: I'm not sure if this is the first but Sword Art Online by Reki Kawahara was one of the first isekai-like story to heavily include video game elements. If it didn't start it, then it at least popularize the 'trapped in a video game trope'. After that, many isekai took video game elements such as levels, interactable menus and unlockable skills, and just included them as part of a real fantasy world, even if that world had nothing to do with video games.
He wrote the first volume in 2001 and published it as a web novel. It was later adapted into other works such as light novels, manga and anime. The 2012 anime was very popular and led to a large spike of isekai stories in general, both in manga and anime.
While this is not a typical isekai and is just a video game world, it had enough cultural impact that it likely was a catalyst for this trope. Many do consider this an isekai (although the author does not) there are also series like Log Horizon which include people sent to a fantasy world that is just like the game they play. Many isekai began blurring these lines so it's hard to find a definitive start to this concept.
Side point but, personally I believe this became a popular trope because its a very explicit way to communicate how strong characters are and a simple way to indicate growth throughout the series.
