Long story short. I told a recruiter that I will tell him when I'm available to have a 15 min talk. Yesterday night I sent him an email asking whether we can chat online today afternoon. I never heard from him again and today afternoon is approaching soon. Does that mean he's offended?
I'd consider it a long shot that he is offended. However, in setting such a short time period, if the recruiter is on vacation or ill then it may be that he isn't checking his e-mail is something you may want to consider here.
I would likely consider giving him a call in the afternoon and leaving a voice mail that you said you'd follow-up. Then it becomes for him to try to let you know some time in his schedule to chat. Sometimes these miscommunications can happen.
Does that mean he's offended?
Only the recruiter can tell you if he is offended or not.
It might depend on the manner in which you told him that you "will tell him when I'm available to have a 15 min talk".
For example, you might have said "I'd really like to talk with you. Let me get back to you quickly with a time that's convenient for me." And you might have sent the email that night.
Or you might have said "No, you don't tell me when you're available to talk, I'll tell you when I'm available to talk." And you might have waited a week to respond.
Or, he might not have received your email.
Or, he might have moved on to another candidate when you weren't available to talk with him initially.
Or he may not be available for a call on such short notice.
Or something else.
You should give him a quick call as soon as practical (and perhaps within the "today afternoon" window). When you eventually connect with him, you can ask if your email came off in a way you didn't intend. And you can asking him the status of the job in question.
As others have pointed out, it's really difficult to tell whether the person is offended or not. While it's very common for someone in your position to think along those lines, here are the other reasons he might not have replied to your email -
He might not have checked your email at all - Probably he's not well or he's on vacation
He did check your email, but either he forgot to reply you or something interrupted him while he was typing in the reply or it could be something else altogether.
In such cases, recruiter's reply to that email would probably be an important event for that day and hence you would be monitoring your mailbox for the same. But for the recruiter, this may not be true as he might have been busy in few other things and this would be just another task for him and there could be other important tasks he has on his plate.
Just a thought.