I had to look this up, but Globe Life is the most recent corporate addition to MLB. They pay $11M/yr for naming rights. In payroll terms, that's not moving the dial very much. And it will only become increasingly marginalized over the 25 year span of their agreement with the Rangers. Sure, it's nice to have that contribution each year, but I don't see how it really affects anything on the field.
$11M/yr is a drop in the bucket for the Rangers, but lately that's been 15-20% of the Orioles' player payroll.
Also, like most long-term contracts I suspect that $11M is just the average annual value of the deal, and the Rangers are probably getting less than that now, but will get more than that per year towards the end of the term.