As a visibly straight, white, cisgendered, able-bodied, adult male, my life is pretty rad.
If I walk through a public park at night, I have no reasonable fear of kidnapping and rape. If I'm stopped by a police officer, I have no reasonable fear that I'll be subjected to unnecessary use of force. If I use a public restroom, I have no reasonable fear that my presence will be challenged (despite my predilection to pee while sitting down).
Now, a lot of left-wingy SJW types would categorize these as "privileges", but I disagree. I think that they are rights. They are rights that I have a right to.
Moreover, I'd like a few more rights. I'd like to feel as safe from rape in, say, prison as I do in a public park. I'd like to have a right to unfiltered Internet access at all times. I'd like to be confident, in a job interview, that I'm being considered purely on my ability to perform the job in question, and not on my views or my personal life.
To the extent that I am in favour of and advocate for said rights, I suppose, yes, that you could call me a Men's Rights Activist.
Now, the reason that I categorize all of the above as rights and not as privileges is that privileges are gifts, bestowed by an authority. Privileges can be doled out arbitrarily, and can be revoked just as arbitrarily. To say that not being raped in a park is a privilege is to imply that I could have that privilege taken away. I am not in favour of this interpretation.
In contrast, a right is not something given - it is something inherent. Authority figures might fail to recognize your right to free speech, or your right to freedom of religion, or your right to a fair trial, but they can never truly take those rights away from you. You have your rights purely by virtue of being a sapient hominid, and although they may be violated or ignored, they can never be erased. They are part and parcel with your personhood.
So, rather than advocating the erasure of privilege, I advocate the recognition of rights. We all have a right not to be sexually assaulted. We all have a right to be treated fairly by the police. We all have a right to pee wherever and however and with whomever we choose.
And no, I don't think it's just semantics. This is important stuff. Terminology matters.
That being said, I'm 100% okay with MRAs - particularly, the unlikely concept of a transmale MRA - being the punchline in this strip. Many of the dudes and organizations that commonly use the title are lousy at being Rights Activists, and laughing at them is an appropriate response.