How many pounds of roast is this recipe for?

ALWAYS cook to Temperature NOT time. (With pretty much everything- not just expensive roasts.)
Keep in mind that it does continue to rise in temperature as it rests. You can always cook it more,but you cannot uncook it.

If you follow the hyperlink to the recipe author (double8cattle) profile, you'll see a link to their website which is a retail beef store. There you will see that their roast product called for in the recipe is listed between 2.5 and 3.5 lbs (3 lbs. average).

Since this recipe is for 6 servings, that's 1/2 lb. per person which is very typical.

If you're cooking for 8, you'll have to decide yourself whether to A.) make the recipe as is and serve slightly smaller portions, B.) cook two smaller roasts and have leftovers, or C.) scour around for a 4 lb. bottom round roast (might be a special order product from your local butcher).

As mentioned by Nancy, use internal temperature for doneness.

Personally, I would serve a smaller portion and add something else to the menu. This is your call though since it will be your dinner table guests not mine so choose wisely.

Best of luck.

Aren't you all lucky to be having that main dish?!
I haven't had the pleasure, so I'm going by second hand knowledge from classes or online recipes. If you hear from others with real experience, go with their advice.
On cooking, many caution against overcooking this cut and strongly recommend cooking to no more than medium doneness (145F internal). So use temp not time as your guide.
On serving size. For this luxury meat, you may need to consider both recipe advice and ingredient cost.
Existing recipes recommend 900g or just under 2 lb for 4 people. Or 1800g or just under 4 lb for 8. This also portions half lb raw meat per serving, which is something I've learned to use when writing new meat recipes (allows for shrinkage during cooking, carving, varying appetites, etc.).
But it's a very expensive cut and if you can't spring for the 1800g, make the 900g for the whole group and surround the beef with plenteous sides and possibly other protein (in appetizers, dessert).
Sounds like a special occasion - wishing you a wonderful time!