I would find a good durable carpet and just have the edges bound to make a rug that fits what you want, you can often find remnant pieces at discount carpet stores and have them bound...

At least while I had kids I would do that...

With a long room, and every designer worth their salt will tell you this, you NEED to break it up into functional spaces.

Imagine standing at one end of a bowling alley and trying to carry on a conversation with someone at the other end. That's what trying to make a long room into a single conversation area feels like.

Start with how you want to USE the space. You've said play area and lounge. That's two functions, so there should be two designated areas for it.

Instead of pushing all your furniture against the wall, let a sofa or chair float opposite another sofa. Separate the kids' play area so that you're not yelling over them when you're talking to someone else in your lounge. This will help you wrangle toys into the designated storage spaces, rather than having them hiding out in the lounge area, and tripping over them on your way through between rooms.

See how the rooms below are broken down into separate functional areas:

Hi there! I think your idea to use two 8X10 rugs is the perfect solution. I'm not sure how you plan to furnish the space, but since you want a combination of playroom/TV lounge, could you delineate the two spaces by placing a sofa in the middle of the room? Or, ideally, maybe just past the middle of the room - maybe allow 12' for lounge area and the remainder for playroom? You could also maybe place two Ikea Kallax cubbies behind the sofa (butted up to it) so they look like a console table, then fill the cubbies with toys and bins. I remember the days of accommodating the kids' toys....they have a way of taking over a space! This might help keep most of the playing behind the sofa so that you have a somewhat tidy area in front?