It's part of what it is in the sense that it's an incredibly broad category, and what some people do can look like that. It's hardly an intrinsic part of it, and I can say that I find it really irritating at the table, though thankfully none of my current players are anywhere near that. There's a lot of different approaches to what RPGs look like in practice, many of which are mutually exclusive.I mean one thing I have noticed here is that nobody has suggested that the players who are sitting around chatting or on their phones are not participating in the hobby. The presumable implication is that this behaviour is, in fact, part of what roleplaying is?
As for your tennis analogy, that's a bit narrow. You've got the specific court, the specific game with rules, etc. A better analogy would be something like hiking - which, just sticking to nearby trails from a few parks can range from a 0.8 mile loop around a lake at moderate elevation (admittedly a mile and a half, but I live in a mountain state) to a 26 mile hike up and down a particularly nasty 14er. The hobby extends past that on either end, and the people going on a quarter mile hike through flat terrain in a lowland forest are generally not looking for the same sort of thing as people planning month long treks through mountains. If you're in either of those groups, yes, the other is technically part of what hiking is. That doesn't make them welcome in your personal hiking group, let alone if you're the poor sap expecting a tiny hike in a forest and showing up at some base camp somewhere where everyone else is expecting a multi-day hike and packed accordingly.