DnsMasq proxyDHCP does not work on UEFI environments:

http://lists.thekelleys.org.uk/pipermail/dnsmasq-discuss/2015q4/009907.html

EDIT_1 if you are using the new DnsMasq with UEFI suport then try adding the missing architecture 9

 dhcp-match=set:EFI_ x86-64, option:client-arch, 9


UEFI 64 clients also use 9 as architecture.

EDIT_2

please base your config on this one

 # Don't function as a DNS server:
 port=0
 
 # Log lots of extra information about DHCP transactions.
 log-dhcp
 
 # Set the root directory for files available via FTP.
 tftp-root=/tftpboot
 
 # Disable re-use of the DHCP servername and filename fields as extra
 # option space. That's to avoid confusing some old or broken DHCP clients.
 dhcp-no-override
 
 # The boot filename, Server name, Server Ip Address
 dhcp-boot=bios/pxelinux,,192.168.1.200
 
 # PXE menu. The first part is the text displayed to the user. The second is the timeout, in seconds.
 # pxe-prompt="Booting PXE Client", 1
 
 # The known types are x86PC, PC98, IA64_EFI, Alpha, Arc_x86,
 # Intel_Lean_Client, IA32_EFI, ARM_EFI, BC_EFI, Xscale_EFI and X86-64_EFI
 # This option is first and will be the default if there is no input from the user.
 
 # PXEClient:Arch:00000
 pxe-service=X86PC, "Boot BIOS PXE", bios/pxelinux
 
 # PXEClient:Arch:00007
 pxe-service=BC_EFI, "Boot UEFI PXE-BC", efi64/syslinux.efi
 
 # PXEClient:Arch:00009
 pxe-service=X86-64_EFI, "Boot UEFI PXE-64", efi64/syslinux.efi
 
 dhcp-range=192.168.1.200,proxy,255.255.255.0



Source
https://wiki.fogproject.org/wiki/index.php?title=ProxyDHCP_with_dnsmasq (Adding UEFI support to the basic script)