Long Short-Term Memory (LSTM) and 3D convolution (Conv3D) show impressive results for many video-based applications but require large memory and intensive computing. Motivated by recent works on hardware-algorithmic co-design towards efficient inference, we propose a compact binarized Conv3D-LSTM model architecture called BILLNET, compatible with a highly resource-constrained hardware. Firstly, BILLNET proposes to factorize the costly standard Conv3D by two pointwise convolutions with a grouped convolution in-between. Secondly, BILLNET enables binarized weights and activations via a MUX-OR-gated residual architecture. Finally, to efficiently train BILLNET, we propose a multi-stage training strategy enabling to fully quantize LSTM layers. Results on Jester dataset show that our method can obtain high accuracy with extremely low memory and computational budgets compared to existing Conv3D resource-efficient models.