Using a normal battery instead of a rechargeable is possibly not all that wise. An electronics engineer would know that.
The circuitry is definitely there to charge the battery and eventhough you have put a non-rechargeable battery in, it will still charge it which is probably the reason it is still operating. A normal battery will take an amount of recharging to a point where it will probably leak.
Also The 165mAh rating comparison is invalid. This is based on one charge. You are comparing the non-rechargeable running from 100% to 0% once (how it should be operated). The rechargeable battery can do this many hundreds of times.
All that said, my old E36 remote batteries where never replaced in the 6 years I had it using one key only. The E36 definitely did not charge the remote battery in the key. Not really sure why they changed to rechargeable actually.