While the source code of Rose is open in the sense that it's available to the general public via GitHub, strictly speaking it's not Open Source because there are no license terms which define what you're able to do with it. Since it was published by the author, one could argue that it was meant to be looked at by others, but that's it. Nobody is legally allowed to actually do anything with it (study the code, build the application, distribute the code or the compiled binary, make changes, re-use code, ...).
Licensing code is not an optional hassle in the world that we're living in. It protects both the author (e.g. from claims if the software doesn't do what somebody thought it'd do!) and the interested third party in being sure to comply with what use cases the author intended the software for. Please pick a license for your code. If you want it to be as useful to others as possible without having to deal with pages of legalese, I would suggest a permissive license such as BSD-2-clause or MIT. If you're more into copyleft, consider GPLv2 or GPLv3, or Apache 2.0 for a middle ground.
I'm contributing to a project that provides Open Source software packages across multiple platforms (DragonFlyBSD, FreeBSD, Linux, NetBSD, Solaris/illumos). After having tried out Rose and liking it, I have replaced Surf on one of my older machines with it. I've prepared a port for it, but cannot commit that as long as there is no license that covers distributing the compiled software. I'd be happy to lend a hand and discuss licensing if you happen to have any questions. Thanks for your efforts to make a simple but modern WebKitGTK browser available!