I would define it more as Source Open than Open Source. Their Source is under Afero License but they only use the Acronym followed by a printout of the Apache License trying to trick people into thinkink it's Apache. And their binary MIT License has the addition that you aren't allowed to hide modify any Product or Trademark indentifications. That contradicts the MIT License!
Admittedly, their licensing scheme is a bit strange, but it's very clearly F/OSS. Even in the most restrictive case, it's still the AGPL with additional exemptions.
I'm not sure that the portion under AGPL actually has exemptions. They say in their LICENSE.txt file:
We promise that we will not enforce the copyleft provisions
in AGPL v3.0 against you if your application (a) does not
link to the Mattermost Platform directly, but exclusively
uses the Mattermost Admin Tools and Configuration Files, and
(b) you have not modified, added to or adapted the source code
of Mattermost in a way that results in the creation of a “modified
version” or “work based on” Mattermost as these terms are defined
in the AGPL v3.0 license.
Note that the two conditions necessary to receive the exemption are connected by "and", not "or". The second condition is that you not create a modified work or a work based upon the program as defined in AGPL v3.0.
But by the terms of AGPL itself its copyleft provisions are only applicable to modified versions, so it doesn't appear that there are any circumstances where Mattermost's exemption will actually exempt you from anything.
One license makes networking applications sources available if modified, the other doesn't as far as I'm aware. Not sure why it has 3 "licenses" they really should figure that out. I think they should just say they're AGPL if anything and make any exception a paid license that turns Mattermost into MIT or Apache license or something? But having two licenses is fine, or one license and exemptions, but three and an exemption that doesn't really make sense... Sheesh.