Has anyone seen that when playing multiplyr games in Xbox One, the XBOX responds ICMP requests ...

most likely due to the DDoS attacks, one method of overloading a server is to bombard it with ICMP requests, which are pings, so MS most likely disabled the server from responding to pings to stop the flood of packets and would show up as 100% packet loss
because your Xbox is sending ICMP and the MS server is just refusing to respond to them.

Hey again W3iRDiE! When you have an ICMP-error it means that your router is not responding to the Internet Control Message Protocol (ICMP) requests. ICMP is used to relay messages between your Xbox 360 console and the network, definitely a crucial thing!
Since a wired connection seems to be out of the question, can I have you try restoring your router to the factory defaults? Also, can you run a speed test at speedtest.net and provide us with an image of the results?

Hey there Jah! (and really anyone else who sees this thread!) There are some great steps to help in here, and also here: Xbox 360 ICMP Error | Xbox ICMP
Error.

If between this thread and that guide, it doesn't take care of the issue for you, please make a fresh thread- since the solution can be different depending on your network setup. Thanks!

Try the steps in this article

support.xbox.com/.../router-gateway-not-responding-icmp-responses-979103

N499C, these forums work best when you create a new thread with a first post of your own, as the original poster's problem and solution, although similar, could be very different in detail.
It's great that you're researching here, but the quickest path to a solution is your own new thread. That being said, when you do start that new thread, please start with the steps at

http://support.xbox.com/xbox-live/connecting/router-not-responding-icmp