No they are certainly not open world but wide corridor games with several viable routes. Same goes for the first Far Cry, developed by the same company.

I'm not sure I'd call it a "sandbox" game, but Crysis 1 was definitely an "open world" game.

Crysis 2 was a lot more linear (not a bad thing, in my opinion.)

Crysis 3 was a bit more open world than Crysis 2, but more linear and less "open world" than Crysis 1.

The Crysis Remastered trilogy btw allows you to enjoy Crysis 3 without EA's Origin DRM, and also includes features like ray tracing and DLSS to the games.

Personally, I think Crysis Warhead was my favorite of the series... and GoG is the best place to get that one as it's available DRM free here and isn't included in the Crysis Remastered trilogy.

AFAIK, the term "open world" refers to the kind of in-game environments that give you a whole bunch of locations to explore and travel between in pretty much any order you please. Usually you're also free to choose your objectives, to some extent. RPG elements are important as well, there's hardly an open-world game without those.

In a linear game, on the other hand, you follow a predetermined path, one objective at a time. Whether it's corridors or a whole island - doesn't really matter. As long as you progress level by level, checkpoint by checkpoint, it's linear.

Crytek's FPS-games were the latter, all 4 of them.

As for "sandbox" or not, I've used that word to describe large open arena-like areas in general, no matter the game. Not sure if that's correct usage, but if it is, then most of the Crysis campaign certainly falls into this category. Same with Warhead, a lot less so with Crysis 2.