If we're discussing that word - the label - as the OP uses it in the meme, then yes, it IS logical to use the name to set the boundaries. If we're discussing the legitimacy of the religion in the wider theological context, you're right - you have to go to the source text and discuss the finer points of what's important to Christianity - but guess what, then we start bickering about whether Calvinists and the Lutherans understood the message of Christianity, whether Jesus was a moral compass or a voice for the poor or a straight up activist against Roman occupation, we start discussing the appropriate role of the Old Testament in Christianity - and then we start stripping away the Christian title from a whole bunch of people who would swear to their dying breath that they were Christians.
The meme is very vaguely worded and leaves this REALLY open ended, but I submit that it's arguing this from the approach of the label of Christianity as a word, which, with all due respect, it really doesn't take much to qualify for just the name.