If in 2140, miners don't get profit with transaction fees from their mining and confirmation, they will shut down their ASICs and the network might be less secured.
Partially true, actually. The decrease in the block rewards are far more impactful at the start, 50 -> 25 -> 12.5 -> 6.25, etc. As we go through more halvings, the transaction fees becomes the major composition of the revenue for the miners. By the 10th halving, the block rewards will dwindle down to 0.1BTC per block. Miners who can't afford to mine will probably exit by then.
The game theory isn't affected. The same logic applies, if the miners or attackers stand to gain more from contributing honestly to the network, then there is no concern.