Yes, because it's obviously not happening for anyone else.
When was your last successful 'Send offer' that you can remember?
Oh wait, I just checked, you're a newbie, you haven't sent anything yet.
The 'they disappear for a short while' thing is normal. It's a visual clue that the page is being reloaded with Ajax (so that it doesn't have to reload the list of games from both users at the very top of the page.) It normally ONLY happens when clicking 'Preview offer'. Clicking on 'Send offer' should NOT show a fade-out effect, instead it'll take you to the finalized offer page, with the 'Edit' and 'Cancel' buttons. (Hmm, maybe I should add a visual clue that the offer was successfully sent, BTW...)
So, it's important that you confirm you're seeing the fade-out effect even on the 'Send offer' button, actually.
I develop the site under Opera, which uses Chromium (Chrome) as its engine. That should handle a good 60% of users. The site is also confirmed to work fine in Firefox. IE, normally should work on recent versions... Can't make promises for IE 6-7. Then again, they have like a 0.1% market share altogether...