Baldwin is widely seen as a shoo-in in for best supporting actor in a comedy show, while McCarthy is the favourite for best guest actress, but faces competition from "Star Wars" legend Carrie Fisher, who would be a poignant posthumous recipient.
McGregor got a second nomination for his narration of Wild Scotland while Rhys and Ahmed were also nominated for their guest appearances on Girls.
Television Academy Chairman Hayma Washington noted the "explosive growth" in television, where more than 400 scripted shows vie for attention across streaming, cable and broadcast networks.
The Primetime Emmy Awards will be handed out September 17.
Industry watchers had predicted a wide open race, with awards juggernaut "Game of Thrones" out of the running - and that prediction was borne out.
However, the network will still be competing in the drama category thanks to its newer show "Westworld", which will go up against other top performers from streaming services, including three series from Netflix - "House of Cards", "The Crown" and "Stranger Things".
Samira Wiley received a nomination in the Supporting Actress, Drama Series category for her portrayal of best friend Moira in Hulu's The Handmaid's Tale. That's the same as past year with the addition of the nomination for Sykes. Snapshot: four of the six nominees for Best Actress in a Drama are from streaming shows.
Riz Ahmed, Ewan McGregor, Geoffrey Rush and John Turturro were also nominated, alongside Benedict Cumberbatch.
The ensemble family drama earned major nominations in the acting categories, as well, with two lead actor nominations for first-time nominee Milo Ventimiglia and Sterling K. Brown, who is hot off a 2016 Emmy win for supporting actor in a limited series for his work on "The People v. O.J. Simpson: American Crime Story", plus supporting nods for both Chrissy Metz and Ron Cephas Jones.
"Game of Thrones" made television history previous year, becoming the most decorated fictional show since the awards began almost seven decades ago with nine awards in technical categories and three top prizes.
In addition to being set in Pittsburgh, show creator Dan Fogelman lived in Bethel Park as a child and used that experience to shape the show.