Assuming I am not speaking to a spammer (the posters above appear to have this a key word, and we are now on an old thread with you as a shiny new user and avatar set up).
Not all devices will have proxy settings, and some things, especially security, might bypass any device level settings in a bid to keep it that way.
People wanting to examine traffic will quite often route things through a server that goes out to the world (a proxy by any other name) that they control so as to be able to examine (sniff) data. It is fairly common in PC sides of things and older devices, but as noted above by the OP then a lot of things these days will use security as it is basically free at this point rather than a real demand on host and server and makes anything other that traffic volume and destination tests, or software lag switches I guess, kind of useless. That said the 3ds did see those pokemon scanners -- seems gamefreak or whatever broadcast the pokemon selection in plain text before the other player user had picked theirs (as in yes you can know basically everything, some were using related values found in similar things to figure out things to do with shinies, and use it to make a counter team, later an update happened to correct it but that it happened at all... Also with the 3ds being in total control of the hackers these days you can probably grab the relevant session keys* to do a decode, at which point we are off to the races with all the analysis of packets people can desire** (most likely after the fact but find where the session keys are in memory and as you can real time debug for cheat search you can probably do real time after grabbing the session key).
*for those unfamiliar with network security then while internet servers do support asymmetric encryption (one key to encode, another to decode, as opposed to symmetric which uses the same key for both encoding and decoding, cheap but you have to keep it hidden which you can not expect to happen for everything long term) it is expensive on resources. To that end most programs will not use that for all the communications and instead have the host send their own new key, one only valid for the given session hence session key, encrypted with the server's public key, the server is then the only thing that decodes it and the server and client program can then communicate using said session key.
**I am not entirely sure what people want here. Cheats is a possibility, manipulation another, hidden info from the game also is potentially shared via it and with enough analysis you might be able to replicate the protocol (some servers will have their own data and calculations happen, many more are matchmaking and packet sharing -- your home ADSL connection will probably struggle to send out packets to 16 people for a game, big server farm is nothing) to make your own servers -- free, no bans beyond those you want, no cheat detection unless you want that... see the DS and Wii wifi play restoration things. I do have a post around here that covers the theory such things in more detail
https://gbatemp.net/threads/private-servers-for-online-gaming.511311/#post-8144717
Better setups will use a computer they control as an access point and manually grab data as it goes out over the wire, others will route traffic on the network through it (that was the gateway aspect), or do something similar with ARP poisoning which does much the same thing, just more doable on consumer grade networking gear. You may also need to go for Linux or Windows server -- consumer versions of Windows post XP... might even have been SP1 when raw sockets was dropped tend to have very limited options for serious network fiddling.