Personally, I wouldn't apply. For most major airlines, the metric that matters above most other qualifications is years of 121 experience. Obviously, they look at your whole resume and body of work, but if you don't have any 121 experience under your belt, your application won't even make it to HR (the ATS will discard it). Even though that job description says some fights will be conducted under part 121, Pentastar is a business aviation company, and as such, won't be counted as a 121 airline by a major. If your goal is to get to a major airline like United, American, Delta (if they ever hire externally again), FedEx, UPS, or Southwest, I wouldn't waste time not accruing 121 experience. It's extremely difficult to be hired by carriers even a tier below the majors (Alaska, JetBlue, Atlas, Spirit, Frontier, etc) without having worked at a 121 shop first. I would say your best bet is to get into a regional, even if it means waiting a few or even several months.
However, if your goal isn't necessarily to make it to a major airline, then dispatching (technically flight following) at the right 135 can be a rewarding career, or at least a path for several years. While at many 135s you will also be a charter coordinator as well, some larger operations such as NetJets (and probably Pentastar, judging from the job description) will have you dispatching similar to a 121. Ultimately, if you want to work in 135, then by all means go for it. However, coming from someone looking to dispatch for one of the aforementioned airlines, I would recommend staying focused exclusively on 121 shops while looking for a place to start - if your goal is the same as mine.
