I wouldn't say they should "forget about" ranking for competitive terms just because they're competitive. I mean,
somebody has to rank highly for competitive terms, so why not them? On the other hand, have they done the testing to find out if those terms convert well? To my mind, it's a waste to spend the time/energy to get rankings for "vanity terms" just so the site owners can brag to their buddies about their rankings. For that matter, it's a waste to chase rankings for rankings sake no matter how easy the terms are to get. As I'm fond of saying, you can't pay the bills with rankings.
What counts are sales and revenue, so before they commit to putting in the work to get traffic on those terms (or any other terms), make sure that traffic is likely to convert.
Have they identified all the additional terms that they want to be ranking for (i.e. "long tail" terms)? Why is their company name the only other term that's been suggested? There should be literally
hundreds of terms on their target search term list.
If they're going to target general and competitive terms, usually the recommendation is to focus the home page on the more general terms and use the interior pages of the site to target more specific terms, as usually the home page is the "strongest" page on the site, so it's in the best position to compete for these generic terms.

I haven't got time for a full review, but right off the bat, I see every page on the site has the same title tag. At a minimum, they need to have unique title tags for each page, with the title tag for that page containing the primary (and if possible secondary) search term for that page. I notice, for instance, that the title tag for the home page doesn't contain either the phrase "payroll software"
or "payroll services".
Second, I don't see the phrases "payroll software" or "payroll services" anywhere in the copy on the home page. As I say, I don't think they need necessarily "forget about" those phrases -- but they might as well forget about ranking for them if the phrases aren't in either the title tag or the on-page text.

Also, the block of tiny, very light gray text at the bottom of the page likely isn't doing them many favors. If it's worthwhile text, then make it easily readable by the people visiting the page. If it's not something they want people to read, get rid of it. As it is, it looks like they've heard that hidden text is bad, and they're trying to hide this without actually making it totally invisible, which just (to me, at least) gives a slightly spammy feel. And there's really no need for that.
My

--Torka