1970s–90s game consoles had extremely limited resolution and color counts (the NES could show about 25 colors on screen). Drawing characters and backgrounds within that constraint naturally meant working pixel-by-pixel on a grid, and the constraint itself became an aesthetic.
Today, with no hardware limits at all, plenty of games still choose it deliberately — indie titles like Stardew Valley and Undertale are the classic examples — both for retro nostalgia and because it lets a small team produce a lot of assets cheaply. Building it for the web needs image-rendering: pixelated so scaling doesn't blur it (the default smooths and mushes pixel boundaries), and pure CSS can even draw a small image by stacking many box-shadow values at pixel-grid coordinates.
Bitmap fonts snapped to the same pixel grid usually accompany it for consistency. It fits games, retro-themed events and a developer's personal site more than serious information-heavy UI.