It's not even Cloudflare, just made to look like it. reCAPTCHA widget is a dead giveaway, real Cloudflare pages use their own implementation.
Edit: oh, I think I've figured out the why! From the JS comments, I think it's used to get around captchas on archived sites (well, at least LinkedIn) sometimes:
var widgetId = grecaptcha.render('g-recaptcha', {
'sitekey': '6LeQbtsSAAAAAHevV56qhVr_0JhQI7N-zTPoOoWJ', // my
//'sitekey': '6Lc7CQMTAAAAAIL84V_tPRYEWZtljsJQJZ5jSijw', // linkedin's
'callback': function(response) {
// [...snip]The alternative would be to use an anti-captcha service that outsources captcha solving to people in low-wage countries, but that's probably a bit expensive given archive.today's scale.