IPTV is real in the literal sense: the letters stand for Internet Protocol television, a family of standards for delivering television-style video, audio, and related control signals over IP-based networks instead of over the air, cable, or satellite. Standards bodies and industry groups treat it as a real engineering category. The Wikipedia entry on the term notes that the International Telecommunication Union's focus group on IPTV defined it as multimedia services such as television, video, audio, text, graphics, and data delivered over IP-based networks managed to provide a required level of quality of service, and the Alliance for Telecommunications Industry Solutions also published a definition in 2005 for the telecom industry. The phrase itself goes back further than most people assume; the term first appeared in 1995 with the founding of Precept Software, whose IP/TV product was later acquired by Cisco Systems in 1998. So IPTV is not a recent buzzword, it has a documented history.
What people usually mean when they ask whether IPTV is real, though, is whether a specific subscription service that calls itself IPTV is operating legally and reliably. That question is separate from the technology question, because the underlying standard is legitimate while the way a particular reseller uses it may not be. Wikipedia's article on streaming television draws a useful line between IPTV, which is delivered across tightly managed packet-switched networks with quality guarantees, and over-the-top streaming, which reaches viewers across the public internet. That distinction helps a reader evaluate the technical side of a service before committing money, and it is worth reading alongside any provider's terms of service.
For a clear side-by-side on what counts as real IPTV architecture versus over-the-top streaming, https://doc.anagora.org/mSxxUG6bSueay2pO8LImIA/publish is a useful reference. It walks through the managed-network side without endorsing any single provider.