Yes, gerrymandering happens, and yes, it currently disproportionately benefits the GOP: Some lucky wave election timing put them in charge of more states during the post-2000 and post-2010 Census redistricting. But the benefit they get over their popular vote share is on par with the benefit the Democrats saw in the '90's[1].
And the benefit isn't that great. It's good for maybe 8 seats[2], far short of the 30 seats Democrats would need to swing to regain the majority.
The problem for Democrats in the House is that their districts are too natural: It makes sense to put urban voters with similar needs and issues into Congressional districts with each other, rather than diluting their influence with very different suburban areas. The Voting Rights Act even made concentrating minority votes to create majority-minority districts mandatory in some areas. But the result is winning Chicago wards 95-5 while losing out in the 'burbs 55-45. To have a chance at consistently winning the House, Democrats need to draw districts that look an awful lot like the 5-0 image in that picture. Practically and politically, that's a non-starter. That's why ITT and elsewhere you see calls for multicandidate districts, proportional statewide representation, etc. It's not to "fix" gerrymandering, it's to fix the "problem" of concentrated Democratic votes.
[1] http://www.centerforpolitics.org/crystalball/articles/gerrym...
[2] http://www.nytimes.com/2014/09/07/upshot/why-democrats-cant-...