I would use Go Button from Figure 53 (only works on Apple devices) for your playback. Free if you only are doing one show. Works with a variety of remotes, which you could sew into your costume or something. Turn-key solution and rock solid. I’ve used it for several shows/events. Source: over 2 years ago

Go Button, by the same people who make QLab. Good enough that I've run a couple of simple shows on it. Source: over 2 years ago

My usual suggestion would be gobutton but it's iOS only. I'd be surprised that you couldn't use some similar keywords to come up with an Android app. Source: about 3 years ago

Https://tabletopia.com/ seems to be a freemium platform for playing many (all?) commercial boardgames and also many standard card games: hearts, bridge, whist, poker etc. And appears to simulate a tabletop for playing with others or solo. I have not played it much but it seems intuitive as a platform for playing many different boardgames online, but is a bit clunky compared to a purpose-built online game. - Source: Hacker News / 6 months ago

Tabletopia. Web app, not many wargames available, I think. Game search is pretty rudimentary. Source: about 1 year ago

Tabletopia - Free to start. Build games through their online editor. Source: about 1 year ago

Maybe look at finding online options for the "more strategic and lengthy board games"? I know there are lots of options for Diplomacy (which is especially suitable for online play, having discrete turns), but I'm sure you'll be able to find similar online portals for other games (e.g. https://tabletopia.com). Source: over 1 year ago

Boardgamearena.com and https://tabletopia.com/ have several more games for free as well. Table Top Simulator itself isn't free, but it does have a ton of free mods for board games. Source: over 1 year ago