Depends on your definition. I've always like this chart which is updated every couple years:
http://www.lboro.ac.uk/gawc/world2016t.html
No, Calgary isn't an Alpha city (it'll never be New York, London, Sydney, etc) but it is a Beta city, similar in importance and "world relevance" to Seattle, Denver, Manchester, Edinburgh, etc. A small step below Berlin or Philly, but a small step above Glasgow or St Petersburg. In addition, Calgary consistently ranks very high in the quality of life it provides.
So, it's not the top of it's class, but Calgary is a pretty important and successful city in its own right, and ranks very well among other cities in the world. Part of getting there and staying there is our infrastructure and development. Having major entertainment venues and surrounding developed areas is just part of that, unfortunately.
I still don't want them spending money on a new arena, but I'm ok with money spent on redevelopment in areas that have a lot of potential (like the plan B area). So we'll see where the funding comes from and goes towards.