A few points : The collison apparently occurred in Bamako FIR , so under control of Bamako ATC, not Senegal, so no need to mention Senegal ATC.
Reading the info like you do, the non-radar coverage is not the issue, even under procedural control ( like most of Africa is) 2 aircraft should not be at the same altitude at the same time, but if they did this is not necessarily due to ATC : levels busts, direct or avoidance tracks taken without advising ATC , etc do occur too. Let's wait a bit before aportioning blame and responsibilities here.
Looks like at first that at least one of the TCAS was inop, or not on. ( a transponder issue maybe )
Possibly the 737 wing hit the cockpit , disabled both pilots but a/c kept on flying , speciulation at this stage. The HS25 is in the water, will be difficult to retreive I guess, :" Only" 7 pax, French media not mentioning it much this week end, so the chances we'll never know are high I would say
I would love to see and hear the reports of both pilots of the 737 though...