Crytek/Saber are likely remastering other Crysis games in addition to C1. Warhead most likely, C2/C3 possible.

The Crytek press release states:

"Crysis Remastered will focus on the original game’s single-player campaigns".

It also states:

"Starting this summer, Crysis Remastered will be available for PC, Xbox One, PlayStation 4, and for Nintendo Switch."

And:

Crytek to release a remaster of Crysis 1 for PC, Xbox One, PlayStation 4, and Nintendo Switch this summer

Which makes me suspect they might be doing some kind of Master Chief Collection-style release where "Crysis Remastered" is a package that they gradually add the other games to.

https://press.crytek.com/crytek-announces-crysis-remastered

Tim Willits of Saber tweeted:

I always loved Crysis games, and it's exciting to work with Crytek to bring these games to new audiences.

He later tweeted

We will be talking about the remasters more soon. I'm glad people are excited.

https://twitter.com/TimWillits/status/1251545724216631298

There was a 4chan rumour floating around that I actually posted here originally but I later felt it was unsubstantiated so I deleted it. It claimed a number of things including that Warhead being remastered would depend on sales, and also that any potential Crysis 4 would depend on remaster sales. I suspect the 4chan rumour was simply parroting stuff from my breakdown of the March 24 teaser footage, as well as other common rumours like Crysis 3 having canned singleplayer Nomad DLC.

My belief is that Crysis 4 is likely in development as the unannounced AAA game Crytek have been working on since last year. I think these remasters are designed to rebuild hype for and trust in the Crysis brand and introduce it to new potential customers. I think any Crysis MP experience is likely to be attached to Crysis 4. I think that the SpacialOS collaboration Crytek announced in early 2019 might be related to that.

Like I say in the title, I think Crysis+Warhead is likely the starting point. I think Crysis 2 and 3 remasters are definitely possible. Crysis 2 in particular has a very strong fanbase. But a C2 remaster would be a more complex undertaking, especially if they're looking to address design complaints. And C3's problem is that the game felt unfinished. It's too short, way too much important story stuff connecting C1/C2/C3 is told in journal entries, the bow is insanely unbalanced, etc. It developed a fanbase over the years, but it's not as well liked as Crysis 2 is among the console fanbase, and not as well liked as Crysis 1/Warhead among PC fans.