This list of clubs and stations with their flight statistics is from last June. Looks like Vegas has only 1 other airport busier than it without an Admirals Club: Columbus/CMH
https://www.flyertalk.com/forum/28380060-post13.html

Originally Posted by AAerSTL
Sunday, June 4, 2017:

1. AA DFW 761 (CLUB)
2. AA CLT 662 (CLUB)
3. AA ORD 474 (CLUB)
4. AA PHL 384 (CLUB)
5. AA MIA 340 (CLUB)
6. AA PHX 292 (CLUB)
7. AA DCA 235 (CLUB)
8. AA LAX 208 (CLUB)
9. AA LGA 141 (CLUB)
10. AA JFK 97 (CLUB)
11. AA BOS 85 (CLUB)
12. AA SFO 53 (CLUB)
13. AA MCO 52 (CLUB)
14. AA RDU 52 (CLUB)
15. AA CMH 47
16. AA ATL 46 (CLUB)
17. AA BNA 46 (CLUB)
18. AA LAS 45
19. AA PIT 43 (CLUB)
20. AA STL 40 (CLUB)
21. AA IND 39
22. AA DTW 38
23. AA DEN 36 (CLUB)
24. AA TPA 36 (CLUB)
25. AA IAH 35 (CLUB)
26. AA SAN 34 (CLUB - CONTRACT)
27. AA SEA 33 (CLUB)
28. AA AUS 32 (CLUB)
29. AA CVG 32
30. AA CLE 31