Essentially, the people who've opined have agreed that it's better to avoid having one-line lead-ins or section headings before longer lead-ins, especially when a table of contents will be automatically inserted in longer articles (i.e. those with more section headings) and force readers who aren't on mobile platfoms to scroll down in search of important information. Therefore, it's better for the lead-in to an article not to include a header.
In other words, keep following the format you've been using, but leave out the Game Info header. Thanks again for your contributions and detailed edit summaries!