From what I can tell, as of writing, Kirkland has a share price around $42 and a market capitalization of around $8.8B, implying around 200M outstanding shares ($8.8B/$42, rounded to one significant figure; I'm getting the share price an market cap from different sources, so I'm not confident that they're reflecting the same exact point in time), with the numbers being around $18, $4.4B and 250M for Detour Gold.
If Kirkland buys Detour for $4.5B (I have no idea what the actual number is, it is probably slightly larger than market cap, as acquisitions tend to be at a premium), and they want to do it with shares, then they will, at current share price (note that acquisitions can introduce a lot of volatility into share price, so this is another area of uncertainty), need $4.5B/42 = 107M shares. So they will go from a ~$9B company with ~200M shares outstanding to a ~13B company with ~300M shares outstanding. Since $18/$42 ~=.43, owners of Detour shares will get around .43 shares of Kirkland for every share of Detour share they currently have. This might be what you're getting at when you say " ANd because Kirkland's share price before the offer was trading at a premium, this afforded them the currency to buy more of Detour ?": the higher the price of Kirkland shares compared to Detour, the fewer shares of Kirkland need to be given for each one of Detour.
The result is in many sense effectively a merger: instead of there being two separate companies, with people owning shares in one or the other, there will be one company with shareholder of the previous companies now owning shares of the merged company.
Kirkland is essentially giving up ownership to a portion of itself over to Detour Gold.
Sort of kind of. Rounding the market caps to $9B and $4.5B, the Detour shareholders will end up with 4.5/(9+4.5) = 33% ownership of the merged company. You can think of that as going from owning all of Detour and none of Kirkland, to owning one-third of both. Kirkland shareholders, meanwhile, will own two-thirds of both. So there is some sense in which Kirkland shareholders are giving up one third of their ownership of Kirkland to get two thirds of Detour. Of course, once this goes through, there won't be a distinction between owning Kirkland versus owning Detour.